@Book{Andrews1998Book,
  author    = {Andrews, George E.},
  publisher = {Cambridge University Press, Cambridge},
  title     = {The theory of partitions},
  year      = {1998},
  isbn      = {0-521-63766-X},
  note      = {Reprint of the 1976 original},
  series    = {Cambridge Mathematical Library},
  file      = {:The theory of partitions.pdf:PDF},
  mrclass   = {11P81 (05A17 11P82 11P83)},
  mrnumber  = {1634067},
  pages     = {xvi+255},
}

@Article{AvalBergeronGarsia2015Polyominoes,
  author        = {Aval, Jean-Christophe and Bergeron, Fran\c{c}ois. and Garsia, Adriano M.},
  journal       = {J. Combin. Theory Ser. A},
  title         = {Combinatorics of labelled parallelogram polyominoes},
  year          = {2015},
  issn          = {0097-3165},
  pages         = {32--57},
  volume        = {132},
  bdsk-url-1    = {https://doi.org/10.1016/j.jcta.2014.12.003},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Combinatorics of labeled parallelogram polyominoes.pdf:PDF},
  fjournal      = {Journal of Combinatorial Theory. Series A},
  mrclass       = {05B50 (05E05)},
  mrnumber      = {3311337},
  mrreviewer    = {Ira Gessel},
  url           = {https://doi.org/10.1016/j.jcta.2014.12.003},
}

@Article{AvalDAdderioDukesHicksLeBorgne2014Polyominoes,
  author        = {Aval, Jean-Christophe and D'Adderio, Michele and Dukes, Mark and Hicks, Angela and Le Borgne, Yvan},
  journal       = {J. Combin. Theory Ser. A},
  title         = {Statistics on parallelogram polyominoes and a {$q,t$}-analogue of the {N}arayana numbers},
  year          = {2014},
  issn          = {0097-3165},
  pages         = {271--286},
  volume        = {123},
  bdsk-url-1    = {https://doi.org/10.1016/j.jcta.2013.09.001},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Statistics on Parallelogram Polyominoes and a q,t-Analogue of the Narayana Numbers.pdf:PDF},
  fjournal      = {Journal of Combinatorial Theory. Series A},
  mrclass       = {05B50 (05E05)},
  mrnumber      = {3157811},
  mrreviewer    = {Anton Vladimirovich Shutov},
  url           = {https://doi.org/10.1016/j.jcta.2013.09.001},
}

 
@Article{BakTangWiesenfeld1987GParking,
  author     = {Bak, Per and Tang, Chao and Wiesenfeld, Kurt},
  journal    = {Physical Review Letters},
  title      = {Self-organized criticality: {An} explanation of the 1/f noise},
  year       = {1987},
  month      = jul,
  number     = {4},
  pages      = {381--384},
  volume     = {59},
  abstract   = {We show that dynamical systems with spatial degrees of freedom naturally evolve into a self-organized critical point. Flicker noise, or 1/f noise, can be identified with the dynamics of the critical state. This picture also yields insight into the origin of fractal objects.},
  doi        = {10.1103/PhysRevLett.59.381},
  file       = {Full Text PDF:https\://journals.aps.org/prl/pdf/10.1103/PhysRevLett.59.381:application/pdf},
  publisher  = {American Physical Society},
  shorttitle = {Self-organized criticality},
  url        = {https://link.aps.org/doi/10.1103/PhysRevLett.59.381},
  urldate    = {2022-03-17},
}

 
@Article{BenkartColmenarejoHarrisOrellanaPanovaSchillingYip2018MinimajPreservingCrystal,
  author   = {Benkart, Georgia and Colmenarejo, Laura and Harris, Pamela E. and Orellana, Rosa and Panova, Greta and Schilling, Anne and Yip, Martha},
  journal  = {Advances in Applied Mathematics},
  title    = {A minimaj-preserving crystal on ordered multiset partitions},
  year     = {2018},
  issn     = {0196-8858},
  month    = apr,
  pages    = {96--115},
  volume   = {95},
  abstract = {We provide a crystal structure on the set of ordered multiset partitions, which recently arose in the pursuit of the Delta Conjecture. This conjecture was stated by Haglund, Remmel and Wilson as a generalization of the Shuffle Conjecture. Various statistics on ordered multiset partitions arise in the combinatorial analysis of the Delta Conjecture, one of them being the minimaj statistic, which is a variant of the major index statistic on words. Our crystal has the property that the minimaj statistic is constant on connected components of the crystal. In particular, this yields another proof of the Schur positivity of the graded Frobenius series of the generalization Rn,k due to Haglund, Rhoades and Shimozono of the coinvariant algebra Rn. The crystal structure also enables us to demonstrate the equidistributivity of the minimaj statistic with the major index statistic on ordered multiset partitions.},
  doi      = {10.1016/j.aam.2017.11.006},
  file     = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/S0196885817301501/pdfft?md5=cc8b2156ee87431c5c11b4e29937b78e&pid=1-s2.0-S0196885817301501-main.pdf&isDTMRedir=Y:application/pdf},
  keywords = {Delta Conjecture, Ordered multiset partitions, Minimaj statistic, Crystal bases, Equidistribution of statistics},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S0196885817301501},
  urldate  = {2022-10-15},
}
 
@Article{Bergeron2020,
       author = {{Bergeron}, Fran{\c{c}}ois},
        title = "{The Bosonic-Fermionic Diagonal Coinvariant Modules Conjecture}",
     keywords = {Mathematics - Combinatorics, Mathematics - Representation Theory, 05E05, 05E10, 20C30, 20C35},
         year = 2020,
        month = may,
          eid = {arXiv:2005.00924},
        pages = {arXiv:2005.00924},
          doi = {10.48550/arXiv.2005.00924},
archivePrefix = {arXiv},
       eprint = {2005.00924},
 primaryClass = {math.CO},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200500924B},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}


@InCollection{BergeronGarsia1999ScienceFiction,
  author        = {Bergeron, Fran\c{c}ois and Garsia, Adriano M.},
  booktitle     = {Algebraic methods and {$q$}-special functions (Montr\'eal, {QC}, 1996)},
  publisher     = {Amer. Math. Soc., Providence, RI},
  title         = {Science fiction and {M}acdonald's polynomials},
  year          = {1999},
  pages         = {1--52},
  series        = {CRM Proc. Lecture Notes},
  volume        = {22},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  mrclass       = {20C30 (05E05 33D67 81R05)},
  mrnumber      = {1726826},
  mrreviewer    = {Yasmine B. Sanderson},
}

@Article{BergeronGarsiaHaimanTesler1999IdentitiesPositivityConjectures,
  author        = {Bergeron, Fran\c{c}ois and Garsia, Adriano M. and Haiman, Mark and Tesler, Glenn},
  journal       = {Methods Appl. Anal.},
  title         = {Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions},
  year          = {1999},
  issn          = {1073-2772},
  note          = {Dedicated to Richard A. Askey on the occasion of his 65th birthday, Part III},
  number        = {3},
  pages         = {363--420},
  volume        = {6},
  bdsk-url-1    = {https://doi.org/10.4310/MAA.1999.v6.n3.a7},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions.pdf:PDF},
  fjournal      = {Methods and Applications of Analysis},
  mrclass       = {05E05 (33D52)},
  mrnumber      = {1803316},
  mrreviewer    = {Ang\`ele M. Hamel},
  url           = {https://doi.org/10.4310/MAA.1999.v6.n3.a7},
}

 
@Article{BergeronGarsiaSergelLevenXin2016PlethysticOperators,
  author    = {Bergeron, Francois and Garsia, Adriano and Sergel Leven, Emily and Xin, Guoce},
  journal   = {Journal of Combinatorics},
  title     = {Some remarkable new plethystic operators in the theory of {Macdonald} polynomials},
  year      = {2016},
  issn      = {2150-959X},
  number    = {4},
  pages     = {671--714},
  volume    = {7},
  abstract  = {International Press of Boston - publishers of scholarly mathematical and scientific journals and books},
  doi       = {10.4310/JOC.2016.v7.n4.a6},
  file      = {Full Text PDF:https\://www.intlpress.com/site/pub/files/_fulltext/journals/joc/2016/0007/0004/JOC-2016-0007-0004-a006.pdf:application/pdf},
  language  = {EN},
  publisher = {International Press of Boston},
  url       = {https://www.intlpress.com/site/pub/pages/journals/items/joc/content/vols/0007/0004/a006/abstract.php},
  urldate   = {2022-05-16},
}

@Article{BergeronHaglundIraciRomero2023SuperNablaOperator,
  author        = {{Bergeron}, Fran{\c{c}}ois and {Haglund}, Jim and {Iraci}, Alessandro and {Romero}, Marino},
  journal       = {arXiv e-prints},
  title         = {{The super nabla operator}},
  year          = {2023},
  month         = mar,
  pages         = {arXiv:2303.00560},
  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
  adsurl        = {https://ui.adsabs.harvard.edu/abs/2023arXiv230300560B},
  archiveprefix = {arXiv},
  doi           = {10.48550/arXiv.2303.00560},
  eid           = {arXiv:2303.00560},
  eprint        = {2303.00560},
  keywords      = {Mathematics - Combinatorics, 05A17, 05E10, 05E05},
  primaryclass  = {math.CO},
}

@Article{BergeronHaiman2013TableauxFormulasMacdonald,
  author        = {Bergeron, Fran\c{c}ois and Haiman, Mark},
  journal       = {Int J Algebr Comput},
  title         = {Tableaux formulas for {M}acdonald polynomials},
  year          = {2013},
  issn          = {0218-1967},
  number        = {4},
  pages         = {833--852},
  volume        = {23},
  bdsk-url-1    = {https://doi.org/10.1142/S0218196713400122},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  fjournal      = {International Journal of Algebra and Computation},
  mrclass       = {05E05 (05E10 20C30)},
  mrnumber      = {3078059},
  mrreviewer    = {Pasquale Petrullo},
  url           = {https://doi.org/10.1142/S0218196713400122},
}

 
@Article{BlasiakHaimanMorsePunSeelinger2023ProofExtendedDelta,
  author    = {Blasiak, Jonah and Haiman, Mark and Morse, Jennifer and Pun, Anna and Seelinger, George H.},
  journal   = {Forum of Mathematics, Pi},
  title     = {A {Proof} of the {Extended} {Delta} {Conjecture}},
  year      = {2023},
  issn      = {2050-5086},
  pages     = {e6},
  volume    = {11},
  abstract  = {We prove the extended delta conjecture of Haglund, Remmel and Wilson, a combinatorial formula for     ΔhlΔ′ekenΔhlΔ′eken{\textbackslash}Delta \_\{h\_l\}{\textbackslash}Delta ' \_\{e\_k\} e\_\{n\}   , where     Δ′ekΔ′ek{\textbackslash}Delta ' \_\{e\_k\}    and     ΔhlΔhl{\textbackslash}Delta \_\{h\_l\}    are Macdonald eigenoperators and     enene\_n    is an elementary symmetric function. We actually prove a stronger identity of infinite series of     GLmGLm{\textbackslash}operatorname \{{\textbackslash}mathrm \{GL\}\}\_m    characters expressed in terms of LLT series. This is achieved through new results in the theory of the Schiffmann algebra and its action on the algebra of symmetric functions.},
  doi       = {10.1017/fmp.2023.3},
  file      = {:BlasiakHaimanMorsePunSeelinger2023ProofExtendedDelta - A Proof of the Extended Delta Conjecture.pdf:PDF},
  keywords  = {35P15, 58C40, 53A07},
  language  = {en},
  publisher = {Cambridge University Press},
  url       = {https://www.cambridge.org/core/journals/forum-of-mathematics-pi/article/proof-of-the-extended-delta-conjecture/5F8020299D6CB2DEFAD8783FDC66F784},
  urldate   = {2023-03-01},
}

@Article{CanLoehr2006qtSquare,
  author        = {Can, Mahir and Loehr, Nicholas},
  journal       = {J. Combin. Theory Ser. A},
  title         = {A proof of the {$q,t$}-square conjecture},
  year          = {2006},
  issn          = {0097-3165},
  number        = {7},
  pages         = {1419--1434},
  volume        = {113},
  bdsk-url-1    = {https://doi.org/10.1016/j.jcta.2006.01.002},
  date-added    = {2018-01-24 15:43:39 +0000},
  date-modified = {2018-01-24 15:44:22 +0000},
  file          = {:A proof of the q,t-square conjecture.pdf:PDF},
  fjournal      = {Journal of Combinatorial Theory. Series A},
  mrclass       = {05E05 (33D99)},
  mrnumber      = {2259069},
  mrreviewer    = {Eric S. Egge},
  url           = {https://doi.org/10.1016/j.jcta.2006.01.002},
}

@Article{Carlitz1975,
  author   = {Carlitz, L.},
  journal  = {The American Mathematical Monthly},
  title    = {A {Combinatorial} {Property} of \textit{q} -{Eulerian} {Numbers}},
  year     = {1975},
  issn     = {0002-9890, 1930-0972},
  month    = jan,
  number   = {1},
  pages    = {51--54},
  volume   = {82},
  abstract = {(1975). A Combinatorial Property of q-Eulerian Numbers. The American Mathematical Monthly: Vol. 82, No. 1, pp. 51-54.},
  doi      = {10.1080/00029890.1975.11993769},
  file     = {:Carlitz1975 - A Combinatorial Property of Q Eulerian Numbers.html:URL},
  language = {en},
  url      = {https://www.tandfonline.com/doi/full/10.1080/00029890.1975.11993769},
  urldate  = {2023-09-28},
}

@Article{CarlssonMellit2018ShuffleConjecture,
  author     = {Carlsson, Erik and Mellit, Anton},
  journal    = {J. Amer. Math. Soc.},
  title      = {A proof of the shuffle conjecture},
  year       = {2018},
  issn       = {0894-0347},
  number     = {3},
  pages      = {661--697},
  volume     = {31},
  bdsk-url-1 = {https://doi.org/10.1090/jams/893},
  doi        = {10.1090/jams/893},
  file       = {:A proof of the shuffle conjecture.pdf:PDF},
  fjournal   = {Journal of the American Mathematical Society},
  mrclass    = {05E10 (05A30 05E05 33D52)},
  mrnumber   = {3787405},
  url        = {https://doi.org/10.1090/jams/893},
}

@Article{CarlssonOblomkov2019AffineSchubertCalculus,
  author   = {Carlsson, Erik and Oblomkov, Alexei},
  journal  = {arXiv:1801.09033 [math]},
  title    = {Affine {Schubert} calculus and double coinvariants},
  year     = {2019},
  month    = jun,
  note     = {arXiv: 1801.09033},
  abstract = {We first define an action of the double coinvariant algebra \$DR\_n\$ on the homology of the affine flag variety \${\textbackslash}widetilde\{Fl\}\_n\$ in type \$A\$, and use affine Schubert calculus to prove that it preserves the image of the homology of the rational \$(n,m)\$-affine Springer fiber \$H\_*({\textbackslash}tilde\{S\}\_\{n,m\}){\textbackslash}subset H\_*({\textbackslash}widetilde\{Fl\}\_n)\$ under the pushforward of the inclusion map. In our main result, we define a filtration by \${\textbackslash}mathbb\{Q\}[{\textbackslash}mathbf\{x\}]\$-submodules of \$DR\_n{\textbackslash}cong H\_*({\textbackslash}tilde\{S\}\_\{n,n+1\})\$ indexed by compositions, whose leading terms are the Garsia-Stanton "descent monomials" in the \$y\$-variables. We find an explicit presentation of the subquotients as submodules of the single-variable coinvariant algebra \$R\_n(x){\textbackslash}cong H\_*(Fl\_n)\$, by identifying the leading torus fixed points with a subset \${\textbackslash}mathcal\{H\}{\textbackslash}subset S\_n\$ of the torus fixed points of the regular nilpotent Hessenberg variety, and comparing them to a cell decomposition of \${\textbackslash}tilde\{S\}\_\{n,n+1\}\$ due to Goresky, Kottwitz, and MacPherson. We also discover an explicit monomial basis of \$DR\_n\$, and in particular an independent proof of the Haglund-Loehr formula.},
  annote   = {Comment: 44 pages, the statement of the main result in the introduction is corrected},
  file     = {:Carlsson2019 - Affine Schubert Calculus and Double Coinvariants.pdf:PDF},
  keywords = {Mathematics - Combinatorics, Mathematics - Algebraic Geometry},
  url      = {http://arxiv.org/abs/1801.09033},
  urldate  = {2022-03-21},
}

@Article{CoriLeBorgne2003SandPileModel,
  author   = {Robert Cori and Yvan {Le Borgne}},
  journal  = {Adv Appl Math},
  title    = {The sand-pile model and Tutte polynomials},
  year     = {2003},
  issn     = {0196-8858},
  number   = {1},
  pages    = {44-52},
  volume   = {30},
  abstract = {A new explicit bijection between spanning trees and recurrent configurations of the sand-pile model is given. This mapping is such that the difference between the number of grains on a configuration and the external activity of the associate tree is the number of edges of the graph. It gives a bijective proof of a result of Merino López expressing the generating function of recurrent configurations as an evaluation of the Tutte polynomial.},
  doi      = {https://doi.org/10.1016/S0196-8858(02)00524-9},
  url      = {https://www.sciencedirect.com/science/article/pii/S0196885802005249},
}

@Article{CorteelHaglundMandelshtamMasonWilliams2020CompactFormulasMacdonald,
  author        = {Corteel, Sylvie and Haglund, Jim and Mandelshtam, Olya and Mason, Sarah and Williams, Lauren},
  journal       = {ArXiv e-prints},
  title         = {Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials},
  year          = {2020},
  date-added    = {2021-01-06 16:08:03 +0100},
  date-modified = {2021-01-06 16:08:03 +0100},
}

@Article{CorteelMandelshtamRoberts2020QuasisymmetricMacdonald,
  author        = {Corteel, Sylvie and Mandelshtam, Olya and Roberts, Austin},
  journal       = {ArXiv e-prints},
  title         = {Expanding the quasisymmetric Macdonald polynomials in the fundamental basis},
  year          = {2020},
  date-added    = {2021-01-06 16:08:11 +0100},
  date-modified = {2021-01-06 16:08:11 +0100},
}

@Article{Courtiel2014GeneralNotionActivity,
  author   = {Courtiel, Julien},
  journal  = {ArXiv e-prints},
  title    = {A general notion of activity for the {Tutte} polynomial},
  year     = {2014},
  month    = dec,
  note     = {arXiv: 1412.2081},
  annote   = {Comment: 38 pages, 21 figures},
  file     = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1412.2081.pdf:application/pdf},
  keywords = {Mathematics - Combinatorics},
  url      = {http://arxiv.org/abs/1412.2081},
  urldate  = {2021-09-10},
}

@Article{DAdderioIraci2017ParallelogramPolyominoes,
  author        = {D'Adderio, Michele and Iraci, Alessandro},
  journal       = {ArXiv e-prints},
  title         = {Parallelogram polyominoes, partially labelled {D}yck paths, and the {D}elta conjecture {(Full Version)}},
  year          = {2017},
  month         = dec,
  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
  archiveprefix = {arXiv},
  bdsk-url-1    = {https://arxiv.org/abs/1712.08787},
  date-added    = {2018-01-24 16:17:48 +0000},
  date-modified = {2018-01-24 16:18:37 +0000},
  eprint        = {1712.08787},
  file          = {:Parallelogram polyominoes, partially labelled Dyck paths, and the Delta conjecture.pdf:PDF},
  keywords      = {Mathematics - Combinatorics, 05E05},
  primaryclass  = {math.CO},
  url           = {https://arxiv.org/abs/1712.08787},
}

@Article{DAdderioIraci2019NewDinv,
  author     = {D'Adderio, Michele and Iraci, Alessandro},
  journal    = {Electron J Comb},
  title      = {{The new dinv is not so new}},
  year       = {2019},
  issn       = {1077-8926},
  number     = {3},
  pages      = {P3.48},
  volume     = {26},
  bdsk-url-1 = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i3p48},
  file       = {:The new dinv is not so new.pdf:PDF},
  fjournal   = {Electronic Journal of Combinatorics},
  url        = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i3p48},
}

@Article{DAdderioIraciLeBorgneRomeroVandenWyngaerd2022TieredTrees,
  author   = {D’Adderio, Michele and Iraci, Alessandro and Le Borgne, Yvan and Romero, Marino and Vanden Wyngaerd, Anna},
  journal  = {Int. Math. Res. Not. IMRN},
  title    = {{Tiered Trees and Theta Operators}},
  year     = {2022},
  issn     = {1073-7928},
  month    = {09},
  note     = {rnac258},
  abstract = {{In [10], the authors introduced tiered trees to define combinatorial objects counting absolutely indecomposable representations of certain quivers and torus orbits on certain homogeneous varieties. In this paper, we use Theta operators, introduced in [6], to give a symmetric function formula that enumerates these trees. We then formulate a general conjecture that extends this result, a special case of which might give some insight about how to formulate a unified Delta conjecture [20].}},
  doi      = {10.1093/imrn/rnac258},
  url      = {https://doi.org/10.1093/imrn/rnac258},
}

@Article{DAdderioIraciVandenWyngaerd2019DeltaSquareConjecture,
  author     = {D'Adderio, Michele and Iraci, Alessandro and Vanden Wyngaerd, Anna},
  journal    = {Int. Math. Res. Not.},
  title      = {{The Delta Square Conjecture}},
  year       = {2019},
  issn       = {1073-7928},
  month      = {03},
  number     = {1},
  pages      = {38--84},
  volume     = {2021},
  bdsk-url-1 = {https://doi.org/10.1093/imrn/rnz057},
  doi        = {10.1093/imrn/rnz057},
  eprint     = {rnz057.pdf},
  file       = {:The Delta Square Conjecture.pdf:PDF},
  fjournal   = {International Mathematics Research Notices},
  url        = {https://doi.org/10.1093/imrn/rnz057},
  urldate    = {2022-03-24},
}

@Article{DAdderioIraciVandenWyngaerd2019GeneralizedDeltaSchroeder,
  author     = {D'Adderio, Michele and Iraci, Alessandro and Vanden Wyngaerd, Anna},
  journal    = {Eur J Combin},
  title      = {{The Schröder case of the generalized Delta conjecture}},
  year       = {2019},
  issn       = {0195-6698},
  pages      = {58 - 83},
  volume     = {81},
  bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0195669819300447},
  bdsk-url-2 = {https://doi.org/10.1016/j.ejc.2019.04.004},
  doi        = {https://doi.org/10.1016/j.ejc.2019.04.004},
  file       = {:The Schröder case of the generalized Delta conjecture.pdf:PDF},
  url        = {http://www.sciencedirect.com/science/article/pii/S0195669819300447},
}

@Article{DAdderioIraciVandenWyngaerd2020GeneralizedDeltat0,
  author     = {D'Adderio, Michele and Iraci, Alessandro and Vanden Wyngaerd, Anna},
  journal    = {Eur J Combin},
  title      = {{The generalized Delta conjecture at {$t=0$}}},
  year       = {2020},
  issn       = {0195-6698},
  pages      = {103088},
  volume     = {86},
  bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0195669820300093},
  bdsk-url-2 = {https://doi.org/10.1016/j.ejc.2020.103088},
  doi        = {https://doi.org/10.1016/j.ejc.2020.103088},
  file       = {:The Generalized Delta Conjecture at t=0.pdf:PDF},
  url        = {http://www.sciencedirect.com/science/article/pii/S0195669820300093},
}

@Article{DAdderioIraciVandenWyngaerd2021ThetaOperators,
  author   = {D'Adderio, Michele and Iraci, Alessandro and Vanden Wyngaerd, Anna},
  journal  = {Adv Math},
  title    = {Theta operators, refined {Delta} conjectures, and coinvariants},
  year     = {2021},
  issn     = {0001-8708},
  month    = jan,
  pages    = {107447},
  volume   = {376},
  doi      = {10.1016/j.aim.2020.107447},
  file     = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/S0001870820304758/pdfft?md5=cc15821062d1179c47947bc2a5c569fd&pid=1-s2.0-S0001870820304758-main.pdf&isDTMRedir=Y:application/pdf},
  fjournal = {Advances in Mathematics},
  keywords = {Macdonald polynomials, Delta conjecture, Theta operators, Diagonal coinvariants},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S0001870820304758},
  urldate  = {2021-09-10},
}

@Book{DAdderioIraciVandenWyngaerd2022TheBible,
  author    = {D'Adderio, Michele and Iraci, Alessandro and Vanden Wyngaerd, Anna},
  publisher = {American Mathematical Society},
  title     = {Decorated {Dyck} paths, polyominoes, and the {Delta} conjecture},
  year      = {2022},
  isbn      = {9781470471705 9781470471576},
  month     = jul,
  number    = {1370},
  series    = {Memoirs of the {American} {Mathematical} {Society}},
  volume    = {278},
  abstract  = {Advancing research. Creating connections.},
  doi       = {10.1090/memo/1370},
  file      = {Full Text PDF:https\://www.ams.org/memo/1370/memo1370.pdf:application/pdf},
  issn      = {0065-9266, 1947-6221},
  language  = {en},
  url       = {https://www.ams.org/memo/1370/},
  urldate   = {2022-05-27},
}

 
@Article{DAdderioMellit2022CompositionalDelta,
  author   = {D'Adderio, Michele and Mellit, Anton},
  journal  = {Adv. Math},
  title    = {A proof of the compositional {Delta} conjecture},
  year     = {2022},
  issn     = {0001-8708},
  month    = jun,
  pages    = {108342},
  volume   = {402},
  abstract = {We prove a compositional refinement of the Delta conjecture (rise version) of Haglund, Remmel and Wilson [16] for Δen−k−1′en which was stated in [8] in terms of Theta operators.},
  doi      = {10.1016/j.aim.2022.108342},
  file     = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/S000187082200158X/pdfft?md5=210b43af1c6dc31e78cdad6879e6598c&pid=1-s2.0-S000187082200158X-main.pdf&isDTMRedir=Y:application/pdf},
  keywords = {Delta conjecture, Theta operators, Dyck path algebra, Macdonald polynomials},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S000187082200158X},
  urldate  = {2022-05-31},
}

@Article{DAdderioRomero2023ThetaIdentities,
  author   = {D’Adderio, Michele and Romero, Marino},
  journal  = {Trans. Amer. Math. Soc.},
  title    = {New identities for theta operators},
  year     = {2023},
  issn     = {0002-9947, 1088-6850},
  abstract = {Advancing research. Creating connections.},
  doi      = {10.1090/tran/8911},
  file     = {Full Text PDF:https\://www.ams.org/tran/0000-000-00/S0002-9947-2023-08911-5/S0002-9947-2023-08911-5.pdf:application/pdf},
  language = {en},
  url      = {https://www.ams.org/tran/0000-000-00/S0002-9947-2023-08911-5/},
  urldate  = {2023-06-05},
}

@Article{DAdderioVandenWyngaerd2017DecoratedDyckPaths,
  author        = {D'Adderio, Michele and Vanden Wyngaerd, Anna},
  journal       = {ArXiv e-prints},
  title         = {Decorated {D}yck paths, the {D}elta conjecture, and a new {$q,t$}-square},
  year          = {2017},
  month         = sep,
  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
  archiveprefix = {arXiv},
  bdsk-url-1    = {https://arxiv.org/abs/1709.08736},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  eprint        = {1709.08736},
  file          = {:Decorated Dyck paths, the Delta conjecture, and a new q,t-square.pdf:PDF},
  keywords      = {Mathematics - Combinatorics},
  primaryclass  = {math.CO},
  url           = {https://arxiv.org/abs/1709.08736},
}

 
@Article{Dhar1990Sandpile,
  author    = {Dhar, Deepak},
  journal   = {Physical Review Letters},
  title     = {Self-organized critical state of sandpile automaton models},
  year      = {1990},
  month     = apr,
  number    = {14},
  pages     = {1613--1616},
  volume    = {64},
  abstract  = {We study a general Bak-Tang-Wiesenfeld–type automaton model of self-organized criticality in which the toppling conditions depend on local height, but not on its gradient. We characterize the critical state, and determine its entropy for an arbitrary finite lattice in any dimension. The two-point correlation function is shown to satisfy a linear equation. The spectrum of relaxation times describing the approach to the critical state is also determined exactly.},
  doi       = {10.1103/PhysRevLett.64.1613},
  file      = {Full Text PDF:https\://journals.aps.org/prl/pdf/10.1103/PhysRevLett.64.1613:application/pdf},
  publisher = {American Physical Society},
  url       = {https://link.aps.org/doi/10.1103/PhysRevLett.64.1613},
  urldate   = {2022-03-17},
}

@Article{DongYan2020Tutte,
  author   = {Dong, Fengming and Yan, Sherry H. F.},
  journal  = {ArXiv e-prints},
  title    = {Proving identities on weight polynomials of tiered trees via {Tutte} polynomials},
  year     = {2020},
  month    = mar,
  note     = {arXiv: 2003.00625},
  file     = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2003.00625.pdf:application/pdf},
  keywords = {Mathematics - Combinatorics},
  url      = {http://arxiv.org/abs/2003.00625},
  urldate  = {2021-09-14},
}

@Article{DuaneGarsiaZabrocki2013NewDinv,
  author     = {Duane, Adrian and Garsia, Adriano M. and Zabrocki, Mike},
  journal    = {J Algebr Comb},
  title      = {A new ``dinv'' arising from the two part case of the shuffle conjecture},
  year       = {2013},
  issn       = {0925-9899},
  number     = {4},
  pages      = {683--715},
  volume     = {37},
  bdsk-url-1 = {https://doi.org/10.1007/s10801-012-0382-0},
  doi        = {10.1007/s10801-012-0382-0},
  file       = {:A new ``dinv'' arising from the two part case of the shuffle conjecture.pdf:PDF},
  fjournal   = {Journal of Algebraic Combinatorics. An International Journal},
  mrclass    = {05E05},
  mrnumber   = {3047015},
  mrreviewer = {Edward E. Allen},
  url        = {https://doi.org/10.1007/s10801-012-0382-0},
}

@Article{DuganGlennonGunnellsSteingrimsson2019TieredTreesqEulerian,
  author   = {William Dugan and Sam Glennon and Paul E. Gunnells and Einar Steingrímsson},
  journal  = {J. Combin. Theory Ser. A},
  title    = {Tiered trees, weights, and q-{E}ulerian numbers},
  year     = {2019},
  issn     = {0097-3165},
  pages    = {24-49},
  volume   = {164},
  abstract = {Maxmin trees are labeled trees with the property that each vertex is either a local maximum or a local minimum. Such trees were originally introduced by Postnikov [12], who gave a formula to count them and different combinatorial interpretations for their number. In this paper we generalize this construction and define tiered trees by allowing more than two classes of vertices. Tiered trees arise naturally when counting the absolutely indecomposable representations of certain quivers, and also when one enumerates torus orbits on certain homogeneous varieties. We define a notion of weight for tiered trees and prove bijections between various weight 0 tiered trees and other combinatorial objects; in particular order n weight 0 maxmin trees are naturally in bijection with permutations on n−1 letters. We conclude by using our weight function to define a new q-analogue of the Eulerian numbers.},
  doi      = {https://doi.org/10.1016/j.jcta.2018.12.002},
  keywords = {Maxmin trees, Intransitive trees, Eulerian numbers, -Eulerian numbers, Nonambiguous trees, Permutations},
  url      = {https://www.sciencedirect.com/science/article/pii/S0097316518301663},
}

@Article{DukesLeBorgne2013PolyominoesSandpile,
  author     = {Dukes, Mark and Le Borgne, Yvan},
  journal    = {J. Combin. Theory Ser. A},
  title      = {Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a {$q,t$}-{N}arayana polynomial},
  year       = {2013},
  issn       = {0097-3165},
  number     = {4},
  pages      = {816--842},
  volume     = {120},
  bdsk-url-1 = {https://doi.org/10.1016/j.jcta.2013.01.004},
  doi        = {10.1016/j.jcta.2013.01.004},
  file       = {:Parallelogram polyominoes, the sandpile model on a complete bipartite graph, and a q,t-Narayana polynomial.pdf:PDF},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {05B50},
  mrnumber   = {3022616},
  mrreviewer = {Anton Vladimirovich Shutov},
  url        = {https://doi.org/10.1016/j.jcta.2013.01.004},
}

@Article{DukesSeligSmithSteingrimsson2018TieredTrees,
  author   = {Dukes, Mark and Selig, Thomas and Smith, Jason P. and Steingrimsson, Einar},
  journal  = {ArXiv e-prints},
  title    = {Permutation graphs and the {Abelian} sandpile model, tiered trees and non-ambiguous binary trees},
  year     = {2018},
  month    = oct,
  note     = {arXiv: 1810.02437},
  annote   = {Comment: 21 pages},
  file     = {arXiv Fulltext PDF:https\://arxiv.org/pdf/1810.02437.pdf:application/pdf},
  keywords = {Mathematics - Combinatorics},
  url      = {http://arxiv.org/abs/1810.02437},
  urldate  = {2021-09-10},
}

@Article{EggeHaglundKillpatrickKremer2003SchroderStatistics,
  author        = {Egge, Eric S. and Haglund, James and Killpatrick, Kendra and Kremer, Darla},
  journal       = {Electron J Comb},
  title         = {A {S}chr\"oder generalization of {H}aglund's statistic on {C}atalan paths},
  year          = {2003},
  issn          = {1077-8926},
  pages         = {Research Paper 16, 21},
  volume        = {10},
  bdsk-url-1    = {http://www.combinatorics.org/Volume_10/Abstracts/v10i1r16.html},
  date-added    = {2018-01-25 10:13:40 +0000},
  date-modified = {2018-01-25 10:14:14 +0000},
  file          = {:A Schr{\"o}der generalization of Haglund's statistic on Catalan paths.pdf:PDF},
  fjournal      = {Electronic Journal of Combinatorics},
  mrclass       = {05A15 (05E05)},
  mrnumber      = {1975766},
  mrreviewer    = {Ira Gessel},
  url           = {http://www.combinatorics.org/Volume_10/Abstracts/v10i1r16.html},
}

 
@Article{EggeLoehrWarrington2010QuasisymmetricExpansionsSchur,
  author   = {Egge, Eric and Loehr, Nicholas A. and Warrington, Gregory S.},
  journal  = {European Journal of Combinatorics},
  title    = {From quasisymmetric expansions to {Schur} expansions via a modified inverse {Kostka} matrix},
  year     = {2010},
  issn     = {0195-6698},
  month    = dec,
  number   = {8},
  pages    = {2014--2027},
  volume   = {31},
  abstract = {Every symmetric function f can be written uniquely as a linear combination of Schur functions, say f=∑λxλsλ, and also as a linear combination of fundamental quasisymmetric functions, say f=∑αyαQα. For many choices of f arising in the theory of Macdonald polynomials and related areas, one knows the quasisymmetric coefficients yα and wishes to compute the Schur coefficients xλ. This paper gives a general combinatorial formula expressing each xλ as a linear combination of the yα’s, where each coefficient in this linear combination is +1, −1, or 0. This formula arises by suitably modifying Eğecioğlu and Remmel’s combinatorial interpretation of the inverse Kostka matrix involving special rim-hook tableaux.},
  doi      = {10.1016/j.ejc.2010.05.010},
  file     = {:egge_quasisymmetric_2010 - From Quasisymmetric Expansions to Schur Expansions Via a Modified Inverse Kostka Matrix.html:URL},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S0195669810000685},
  urldate  = {2022-10-26},
}

@Article{GarsiaHaglund2002qtCatalan,
  author        = {Garsia, Adriano M. and Haglund, James},
  journal       = {Discrete Math},
  title         = {A proof of the {$q,t$}-{C}atalan positivity conjecture},
  year          = {2002},
  issn          = {0012-365X},
  note          = {LaCIM 2000 Conference on Combinatorics, Computer Science and Applications (Montreal, QC)},
  number        = {3},
  pages         = {677--717},
  volume        = {256},
  bdsk-url-1    = {https://doi.org/10.1016/S0012-365X(02)00343-6},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:A proof of the q,t-Catalan positivity conjecture.pdf:PDF},
  fjournal      = {Discrete Mathematics},
  mrclass       = {05E05 (05E10 33D45)},
  mrnumber      = {1935784},
  mrreviewer    = {Michael A. Zabrocki},
  url           = {https://doi.org/10.1016/S0012-365X(02)00343-6},
}

@Article{GarsiaHaglundRemmelYoo2019Deltaq0,
  author     = {Garsia, Adriano and Haglund, Jim and Remmel, Jeffrey B. and Yoo, Meesue},
  journal    = {Ann Comb},
  title      = {A {P}roof of the {D}elta {C}onjecture {W}hen {$q=0$}},
  year       = {2019},
  issn       = {0219-3094},
  month      = {Jun},
  number     = {2},
  pages      = {317--333},
  volume     = {23},
  abstract   = {In Haglund et al. (Trans. Amer. Math. Soc. 370(6):4029--4057, 2018), Haglund, Remmel and Wilson introduce a conjecture which gives a combinatorial prediction for the result of applying a certain operator to an elementary symmetric function. This operator, defined in terms of its action on the modified Macdonald basis, has played a role in work of Garsia and Haiman on diagonal harmonics, the Hilbert scheme, and Macdonald polynomials (Garsia and Haiman in J. Algebraic Combin. 5:191--244, 1996; Haiman in Invent. Math. 149:371--407, 2002). The Delta Conjecture involves two parameters q, t; in this article we give the first proof that the Delta Conjecture is true when q=0 or t=0.},
  bdsk-url-1 = {https://doi.org/10.1007/s00026-019-00426-x},
  day        = {01},
  doi        = {10.1007/s00026-019-00426-x},
  file       = {:A Proof of the Delta Conjecture When q=0.pdf:PDF},
  url        = {https://doi.org/10.1007/s00026-019-00426-x},
}

@InCollection{GarsiaHaglundXinZabrocki2016PieriRules,
  author        = {Garsia, Adriano and Haglund, Jim and Xin, Guoce and Zabrocki, Mike},
  booktitle     = {The mathematical legacy of {R}ichard {P}. {S}tanley},
  publisher     = {Amer. Math. Soc., Providence, RI},
  title         = {Some new applications of the {S}tanley-{M}acdonald {P}ieri rules},
  year          = {2016},
  pages         = {141--168},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  mrclass       = {05E05},
  mrnumber      = {3617221},
}

@Article{GarsiaHaiman1993GradedRepresentationModel,
  author        = {Garsia, Adriano M. and Haiman, Mark},
  journal       = {Proc. Nat. Acad. Sci. U.S.A.},
  title         = {A graded representation model for {M}acdonald's polynomials},
  year          = {1993},
  issn          = {0027-8424},
  number        = {8},
  pages         = {3607--3610},
  volume        = {90},
  bdsk-url-1    = {https://doi.org/10.1073/pnas.90.8.3607},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:A graded representation model for Macdonald's polynomials.pdf:PDF},
  fjournal      = {Proceedings of the National Academy of Sciences of the United States of America},
  mrclass       = {05E05 (05E10 20C30)},
  mrnumber      = {1214091},
  mrreviewer    = {John R. Stembridge},
  url           = {https://doi.org/10.1073/pnas.90.8.3607},
}

@Article{GarsiaHaiman1995FactorizationsPieriRules,
  author     = {Garsia, Adriano M. and Haiman, Mark},
  journal    = {Discrete Math},
  title      = {Factorizations of {P}ieri rules for {M}acdonald polynomials},
  year       = {1995},
  issn       = {0012-365X},
  note       = {Formal power series and algebraic combinatorics (Montreal, PQ, 1992)},
  number     = {1-3},
  pages      = {219--256},
  volume     = {139},
  bdsk-url-1 = {https://doi.org/10.1016/0012-365X(94)00134-5},
  doi        = {10.1016/0012-365X(94)00134-5},
  file       = {:Factorizations of Pieri rules for Macdonald polynomials.pdf:PDF},
  fjournal   = {Discrete Mathematics},
  mrclass    = {05E05},
  mrnumber   = {1336841},
  url        = {https://doi.org/10.1016/0012-365X(94)00134-5},
}

@Article{GarsiaHaiman1996qLagrange,
  author        = {Garsia, Adriano M. and Haiman, Mark},
  journal       = {J Algebr Comb},
  title         = {A remarkable {$q,t$}-{C}atalan sequence and {$q$}-{L}agrange inversion},
  year          = {1996},
  issn          = {0925-9899},
  number        = {3},
  pages         = {191--244},
  volume        = {5},
  bdsk-url-1    = {https://doi.org/10.1023/A:1022476211638},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:A Remarkable q,t-Catalan Sequence and q-Lagrange Inversion.pdf:PDF},
  fjournal      = {Journal of Algebraic Combinatorics. An International Journal},
  mrclass       = {05E15 (05A10 05A30 05E10)},
  mrnumber      = {1394305},
  mrreviewer    = {Edward E. Allen},
  url           = {https://doi.org/10.1023/A:1022476211638},
}

@Article{GarsiaHaimanTesler1999ExplicitPlethysticFormulas,
  author        = {Garsia, Adriano M. and Haiman, Mark and Tesler, Glenn},
  journal       = {Sem. Lothar. Combin.},
  title         = {Explicit plethystic formulas for {M}acdonald {$q,t$}-{K}ostka coefficients},
  year          = {1999},
  issn          = {1286-4889},
  note          = {The Andrews Festschrift (Maratea, 1998)},
  pages         = {Art. B42m, 45},
  volume        = {42},
  bdsk-url-1    = {http://elibm.org/ft/10009341003},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Explicit Plethystic Formulas for Macdonald q,t-Kostka coefficients.pdf:PDF},
  fjournal      = {S\'eminaire Lotharingien de Combinatoire},
  mrclass       = {05E05 (33D52)},
  mrnumber      = {1701592},
  mrreviewer    = {Yasmine B. Sanderson},
  url           = {http://elibm.org/ft/10009341003},
}

@Article{GarsiaHicksStout2011Casek2Shuffle,
  author        = {Garsia, Adriano and Hicks, Angela and Stout, Andrew},
  journal       = {J. Comb.},
  title         = {The case {$k=2$} of the {S}huffle {C}onjecture},
  year          = {2011},
  issn          = {2156-3527},
  number        = {2},
  pages         = {193--229},
  volume        = {2},
  bdsk-url-1    = {https://doi.org/10.4310/JOC.2011.v2.n2.a2},
  date-added    = {2018-01-24 16:34:52 +0000},
  date-modified = {2018-01-24 16:35:17 +0000},
  file          = {:The case k=2 of the Shuffle Conjecture.pdf:PDF},
  fjournal      = {Journal of Combinatorics},
  mrclass       = {05A05 (05A15 05E05)},
  mrnumber      = {2913193},
  url           = {https://doi.org/10.4310/JOC.2011.v2.n2.a2},
}

@Article{GarsiaLieseRemmelYoo2018DeltaSchur,
  author        = {Garsia, Adriano M. and Liese, J. and Remmel, Jeffrey B. and Yoo, Meesue},
  journal       = {ArXiv e-prints},
  title         = {Exploring a {D}elta {S}chur {C}onjecture},
  year          = {2018},
  month         = jan,
  archiveprefix = {arXiv},
  bdsk-url-1    = {https://arxiv.org/abs/1801.07385},
  eprint        = {1801.07385},
  file          = {:Exploring a Delta Schur Conjecture.pdf:PDF},
  keywords      = {Mathematics - Combinatorics},
  primaryclass  = {math.CO},
  url           = {https://arxiv.org/abs/1801.07385},
}

@Article{GarsiaTesler1996qtKostka,
  author   = {Garsia, Adriano and Tesler, Glenn},
  journal  = {Adv Math},
  title    = {Plethystic {Formulas} for {Macdonald} {$q,t$}-{Kostka} {Coefficients}},
  year     = {1996},
  issn     = {0001-8708},
  month    = nov,
  number   = {2},
  pages    = {144--222},
  volume   = {123},
  doi      = {10.1006/aima.1996.0071},
  file     = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/S0001870896900717/pdf?md5=bd07cf6ac840c139fbb74cb6d279ced4&pid=1-s2.0-S0001870896900717-main.pdf&isDTMRedir=Y:application/pdf},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S0001870896900717},
  urldate  = {2021-07-26},
}

@Article{GarsiaXinZabrocki2014ThreeShuffle,
  author     = {Garsia, Adriano M. and Xin, Guoce and Zabrocki, Mike},
  journal    = {J. Combin. Theory Ser. A},
  title      = {A three shuffle case of the compositional parking function conjecture},
  year       = {2014},
  issn       = {0097-3165},
  pages      = {202--238},
  volume     = {123},
  bdsk-url-1 = {https://doi.org/10.1016/j.jcta.2013.12.008},
  doi        = {10.1016/j.jcta.2013.12.008},
  file       = {:A three shuffle case of the compositional parking function conjecture.pdf:PDF},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {05E05},
  mrnumber   = {3157808},
  mrreviewer = {Arun Ram},
  url        = {https://doi.org/10.1016/j.jcta.2013.12.008},
}

@Article{GarsiaXinZabrocki2014TwoShuffle,
  author     = {Garsia, Adriano M. and Xin, Guoce and Zabrocki, Mike},
  journal    = {Symmetry: Representation Theory and Its Applications: In Honor of Nolan R. Wallach},
  title      = {Proof of the 2-part compositional shuffle conjecture},
  year       = {2014},
  pages      = {227--257},
  address    = {New York, NY},
  bdsk-url-1 = {https://doi.org/10.1007/978-1-4939-1590-3_8},
  doi        = {10.1007/978-1-4939-1590-3_8},
  file       = {:Proof of the 2-part compositional shuffle conjecture.pdf:PDF},
  isbn       = {978-1-4939-1590-3},
  publisher  = {Springer New York},
  url        = {https://doi.org/10.1007/978-1-4939-1590-3_8},
}

@Article{Gessel1995Graphs,
  author   = {Gessel, Ira M.},
  journal  = {Discrete Math},
  title    = {Enumerative applications of a decomposition for graphs and digraphs},
  year     = {1995},
  issn     = {0012-365X},
  month    = may,
  number   = {1},
  pages    = {257--271},
  volume   = {139},
  abstract = {A simple decomposition for graphs yields generating functions for counting graphs by edges and connected components. A change of variables gives a new interpretation to the Tutte polynomial of the complete graph involving inversions of trees. The relation between the Tutte polynomial of the complete graph and the inversion enumerator for trees is generalized to the Tutte polynomial of an arbitrary graph. When applied to digraphs, the decomposition yields formulas for counting digraphs and acyclic digraphs by edges and initially connected components.},
  doi      = {10.1016/0012-365X(94)00135-6},
  file     = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/0012365X94001356/pdf?md5=7cfd0b766e74c1ac771e689f074add29&pid=1-s2.0-0012365X94001356-main.pdf&isDTMRedir=Y:application/pdf},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/0012365X94001356},
  urldate  = {2021-09-15},
}

@article{Gessel2019,
  author   = {Gessel, Ira M.},
  journal  = {Electron. J. Comb.},
  title    = {On the {Schur} function expansion of a symmetric quasi-symmetric function},
  year     = {2019},
  issn     = {1077-8926},
  number   = {4},
  pages    = {research paper p4.50, 5},
  volume   = {26},
  file     = {:Gessel2019 - On the Schur Function Expansion of a Symmetric Quasi Symmetric Function/Gessel2019 - On the Schur Function Expansion of a Symmetric Quasi Symmetric Function.pdf:PDF},
  fjournal = {The Electronic Journal of Combinatorics},
  keywords = {05E05},
  language = {English},
  url      = {www.combinatorics.org/ojs/index.php/eljc/article/view/v26i4p50},
  zbl      = {1431.05146},
  zbmath   = {7152758},
}

@Article{GillespieRhoades2020SpechtBases,
  author        = {Gillespie, Maria and Rhoades, Brendon},
  journal       = {ArXiv e-prints},
  title         = {Higher {S}pecht bases for generalizations of the coinvariant ring},
  year          = {2020},
  date-added    = {2021-01-06 16:12:53 +0100},
  date-modified = {2021-01-06 16:12:53 +0100},
}

 
@Article{GorskyNegut2015RefinedKnotInvariants,
  author   = {Gorsky, Eugene and Neguţ, Andrei},
  journal  = {Journal de Mathématiques Pures et Appliquées},
  title    = {Refined knot invariants and {Hilbert} schemes},
  year     = {2015},
  issn     = {0021-7824},
  month    = sep,
  number   = {3},
  pages    = {403--435},
  volume   = {104},
  abstract = {We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's conjecture on the stabilization of superpolynomials, and then use the results of O. Schiffmann and E. Vasserot to relate knot invariants to the Hilbert scheme of points on C2. Then we use the methods of the second author to compute these invariants explicitly in the uncolored case. We also propose a conjecture relating these constructions to the rational Cherednik algebra, as in the work of the first author, A. Oblomkov, J. Rasmussen and V. Shende. Among the combinatorial consequences of this work is a statement of the mn shuffle conjecture. Résumé On considere la construction des invariants de Chern–Simons rafinés des noeuds toriques par M. Aganagic et S. Shakirov du point de vue DAHA de I. Cherednik. On démontre une conjecture de Cherednik sur la stabilisation des superpolynômes, et puis on utilise les resultats de O. Schiffmann et E. Vasserot pour relier les invariants des noeuds au schéma d'Hilbert des points sur C2. Ensuite on utilise les techniques du deuxième auteur pour calculer ces invariants explicitement dans le cas non-coloré. On propose aussi une conjecture reliant ces constructions à l'algèbre de Cherednik rationelle, comme dans l'article du premier auteur avec A. Oblomkov, J. Rasmussen et V. Shende. Parmi les conséquences combinatoires de cette étiude on a énoncé de la conjecture de mn battage.},
  doi      = {10.1016/j.matpur.2015.03.003},
  file     = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/S0021782415000367/pdfft?md5=adb2d7477c73f272e99f8cfe160b32a6&pid=1-s2.0-S0021782415000367-main.pdf&isDTMRedir=Y:application/pdf},
  keywords = {Torus knots, Hilbert scheme, Double affine Hecke algebra},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S0021782415000367},
  urldate  = {2022-05-16},
}

@Article{GunnellsLetellierRodriguezVillegas2018Quivers,
  author   = {Gunnells, Paul E. and Letellier, Emmanuel and Rodriguez Villegas, Fernando},
  journal  = {Math. Z.},
  title    = {Torus orbits on homogeneous varieties and {Kac} polynomials of quivers},
  year     = {2018},
  issn     = {1432-1823},
  month    = oct,
  number   = {1},
  pages    = {445--467},
  volume   = {290},
  abstract = {In this paper we prove that the counting polynomials of certain torus orbits in products of partial flag varieties coincides with the Kac polynomials of supernova quivers, which arise in the study of the moduli spaces of certain irregular meromorphic connections on trivial bundles over the projective line. We also prove that these polynomials can be expressed as a specialization of Tutte polynomials of certain graphs providing a new way to compute them. We also discuss connections with the Gel’fand–MacPherson correspondence.},
  doi      = {10.1007/s00209-017-2025-6},
  language = {en},
  url      = {https://doi.org/10.1007/s00209-017-2025-6},
  urldate  = {2021-07-26},
}

@Article{Haglund2003CatalanStatistics,
  author     = {Haglund, James},
  journal    = {Adv Math},
  title      = {Conjectured statistics for the {$q,t$}-{C}atalan numbers},
  year       = {2003},
  issn       = {0001-8708},
  number     = {2},
  pages      = {319--334},
  volume     = {175},
  bdsk-url-1 = {https://doi.org/10.1016/S0001-8708(02)00061-0},
  doi        = {10.1016/S0001-8708(02)00061-0},
  file       = {:Conjectured statistics for the q,t-Catalan numbers.pdf:PDF},
  fjournal   = {Advances in Mathematics},
  mrclass    = {05A30 (05A10 05A15 05A16 05E05)},
  mrnumber   = {1972636},
  mrreviewer = {Shaun Cooper},
  url        = {https://doi.org/10.1016/S0001-8708(02)00061-0},
}

@Article{Haglund2004Schroeder,
  author        = {Haglund, James},
  journal       = {Int Math Res Notices},
  title         = {A {P}roof of the {$q,t$}-{S}chr{\"o}der {C}onjecture},
  year          = {2004},
  issn          = {1073-7928},
  number        = {11},
  pages         = {525--560},
  volume        = {2004},
  bdsk-url-1    = {https://doi.org/10.1155/S1073792804132509},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:A Proof of the q,t-Schr{\"o}der Conjecture.pdf:PDF},
  fjournal      = {International Mathematics Research Notices},
  mrclass       = {05E05 (33D80)},
  mrnumber      = {2038776},
  mrreviewer    = {Edward E. Allen},
  url           = {https://doi.org/10.1155/S1073792804132509},
}

@Article{Haglund2005GenesisMacdonaldStatistics,
  author     = {Haglund, James},
  journal    = {Sem. Lothar. Combin.},
  title      = {The genesis of the {M}acdonald polynomial statistics},
  year       = {2005},
  issn       = {1286-4889},
  pages      = {Art. B54Ao, 16},
  volume     = {54A},
  bdsk-url-1 = {http://elibm.org/ft/10009472001},
  file       = {:The genesis of the Macdonald polynomial statistics.pdf:PDF},
  fjournal   = {S\'eminaire Lotharingien de Combinatoire},
  mrclass    = {05E05},
  mrnumber   = {2223027},
  mrreviewer = {Kendra Killpatrick},
  url        = {http://elibm.org/ft/10009472001},
}

@Book{Haglund2008Book,
  author        = {Haglund, James},
  publisher     = {American Mathematical Society, Providence, RI},
  title         = {The {$q$},{$t$}-{C}atalan numbers and the space of diagonal harmonics},
  year          = {2008},
  isbn          = {978-0-8218-4411-3; 0-8218-4411-3},
  note          = {With an appendix on the combinatorics of Macdonald polynomials},
  series        = {University Lecture Series},
  volume        = {41},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:The q,t-Catalan numbers and the space of diagonal harmonics.pdf:PDF},
  mrclass       = {05E05 (05A05 05A30 33D52)},
  mrnumber      = {2371044},
  mrreviewer    = {Michael A. Zabrocki},
  pages         = {viii+167},
}

@Article{HaglundHaimanLoehr2005CombinatorialFormulaMacdonald,
  author     = {Haglund, James and Haiman, Mark and Loehr, Nicholas},
  journal    = {J. Amer. Math. Soc.},
  title      = {A combinatorial formula for {M}acdonald polynomials},
  year       = {2005},
  issn       = {0894-0347},
  number     = {3},
  pages      = {735--761},
  volume     = {18},
  bdsk-url-1 = {https://doi.org/10.1090/S0894-0347-05-00485-6},
  doi        = {10.1090/S0894-0347-05-00485-6},
  file       = {:A combinatorial formula for Macdonald polynomials.pdf:PDF},
  fjournal   = {Journal of the American Mathematical Society},
  mrclass    = {05E05},
  mrnumber   = {2138143},
  mrreviewer = {Frank Sottile},
  url        = {https://doi.org/10.1090/S0894-0347-05-00485-6},
}

@Article{HaglundHaimanLoehrRemmelUlyanov2005ShuffleConjecture,
  author        = {Haglund, James and Haiman, Mark and Loehr, Nicholas and Remmel, Jeffrey B. and Ulyanov, Anatoly},
  journal       = {Duke Math J},
  title         = {A combinatorial formula for the character of the diagonal coinvariants},
  year          = {2005},
  issn          = {0012-7094},
  number        = {2},
  pages         = {195--232},
  volume        = {126},
  bdsk-url-1    = {https://doi.org/10.1215/S0012-7094-04-12621-1},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:A combinatorial formula for the character of the diagonal coinvariants.pdf:PDF},
  fjournal      = {Duke Mathematical Journal},
  mrclass       = {05E10 (05A30 20C30)},
  mrnumber      = {2115257},
  mrreviewer    = {Edward E. Allen},
  url           = {https://doi.org/10.1215/S0012-7094-04-12621-1},
}

@Article{HaglundLoehr2005HilbertSeriesHarmonics,
  author     = {Haglund, James and Loehr, Nicholas},
  journal    = {Discrete Math},
  title      = {A conjectured combinatorial formula for the {H}ilbert series for diagonal harmonics},
  year       = {2005},
  issn       = {0012-365X},
  note       = {Formal Power Series and Algebraic Combinatorics 2002 (FPSAC'02)},
  number     = {1},
  pages      = {189 - 204},
  volume     = {298},
  bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0012365X05002402},
  bdsk-url-2 = {https://doi.org/10.1016/j.disc.2004.01.022},
  doi        = {https://doi.org/10.1016/j.disc.2004.01.022},
  file       = {:A conjectured combinatorial formula for the Hilbert series for diagonal harmonics.pdf:PDF},
  fjournal   = {Discrete Mathematics},
  keywords   = {Catalan number, Parking functions, Labelled trees, Hilbert series},
  url        = {http://www.sciencedirect.com/science/article/pii/S0012365X05002402},
}

@Article{HaglundMorseZabrocki2012CompositionalShuffleConjecture,
  author        = {Haglund, James and Morse, Jennifer and Zabrocki, Mike},
  journal       = {Canadian J Math},
  title         = {A {C}ompositional {S}huffle {C}onjecture {S}pecifying {T}ouch {P}oints of the {D}yck {P}ath},
  year          = {2012},
  issn          = {0008-414X},
  number        = {4},
  pages         = {822--844},
  volume        = {64},
  bdsk-url-1    = {https://doi.org/10.4153/CJM-2011-078-4},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:A Compositional Shuffle Conjecture Specifying Touch Points of the Dyck Path.pdf:PDF},
  fjournal      = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques},
  mrclass       = {05E05 (33D52)},
  mrnumber      = {2957232},
  mrreviewer    = {Arthur L. B. Yang},
  url           = {https://doi.org/10.4153/CJM-2011-078-4},
}

@Article{HaglundRemmelWilson2018DeltaConjecture,
  author     = {Haglund, James and Remmel, Jeffrey B. and Wilson, Andrew T.},
  journal    = {Trans. Amer. Math. Soc.},
  title      = {The {D}elta {C}onjecture},
  year       = {2018},
  issn       = {0002-9947},
  number     = {6},
  pages      = {4029--4057},
  volume     = {370},
  bdsk-url-1 = {https://doi.org/10.1090/tran/7096},
  doi        = {10.1090/tran/7096},
  file       = {:The Delta Conjecture.pdf:PDF},
  fjournal   = {Transactions of the American Mathematical Society},
  mrclass    = {05E05 (05E10)},
  mrnumber   = {3811519},
  url        = {https://doi.org/10.1090/tran/7096},
}

@Article{HaglundRhoadesShimozono2018OrderedSetPartitions,
  author     = {Haglund, James and Rhoades, Brendon and Shimozono, Mark},
  journal    = {Adv Math},
  title      = {Ordered set partitions, generalized coinvariant algebras, and the {D}elta {C}onjecture},
  year       = {2018},
  issn       = {0001-8708},
  pages      = {851--915},
  volume     = {329},
  bdsk-url-1 = {https://doi.org/10.1016/j.aim.2018.01.028},
  doi        = {10.1016/j.aim.2018.01.028},
  file       = {:Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture.pdf:PDF},
  fjournal   = {Advances in Mathematics},
  mrclass    = {05A18 (05E05)},
  mrnumber   = {3783430},
  url        = {https://doi.org/10.1016/j.aim.2018.01.028},
}

 
@Article{HaglundSergel2021SchedulesDeltaConjecture,
  author   = {Haglund, James and Sergel, Emily},
  journal  = {Annals of Combinatorics},
  title    = {Schedules and the {Delta} {Conjecture}},
  year     = {2021},
  issn     = {0219-3094},
  month    = mar,
  number   = {1},
  pages    = {1--31},
  volume   = {25},
  abstract = {In a recent preprint, Carlsson and Oblomkov (Affine Schubert calculus and double coinvariants. arXiv preprint 1801.09033, 2018) obtain a long sought-after monomial basis for the ring \$\${\textbackslash}mathrm\{D\}{\textbackslash}!{\textbackslash}mathrm\{R\}\_n\$\$of diagonal coinvariants. Their basis is closely related to the “schedules” formula for the Hilbert series of \$\${\textbackslash}mathrm\{D\}{\textbackslash}!{\textbackslash}mathrm\{R\}\_n\$\$which was conjectured by the first author and Loehr (Discete Math 298(1–3):189–204, 2005) and first proved by Carlsson and Mellit (A proof of the shuffle conjecture. J Amer Math Soc 31(3):661–697, 2018), as a consequence of their proof of the famous Shuffle Conjecture. In this article, we obtain a schedules formula for the combinatorial side of the Delta Conjecture, a conjecture introduced by the Haglund et al. (Trans Am Math Soc 370(6):4029–4057, 2018), which contains the Shuffle Theorem as a special case. Motivated by the Carlsson–Oblomkov basis for \$\${\textbackslash}mathrm\{D\}{\textbackslash}!{\textbackslash}mathrm\{R\}\_n\$\$and our Delta schedules formula, we introduce a (conjectural) basis for the super-diagonal coinvariant ring \$\${\textbackslash}mathrm\{S\}{\textbackslash}!{\textbackslash}mathrm\{D\}{\textbackslash}!{\textbackslash}mathrm\{R\}\_n\$\$, an \$\$S\_n\$\$-module generalizing \$\${\textbackslash}mathrm\{D\}{\textbackslash}!{\textbackslash}mathrm\{R\}\_n\$\$introduced recently by Zabrocki (a module for the Delta conjecture. arXiv preprint 1902.08966, 2019), which conjecturally corresponds to the Delta Conjecture.},
  doi      = {10.1007/s00026-020-00517-0},
  file     = {:Haglund2021 - Schedules and the Delta Conjecture.html:URL},
  language = {en},
  url      = {https://doi.org/10.1007/s00026-020-00517-0},
  urldate  = {2022-03-21},
}

@Article{HaglundXin2017LectureNotes,
  author        = {Haglund, James and Xin, Guoce},
  journal       = {ArXiv e-prints},
  title         = {Lecture notes on the {C}arlsson-{M}ellit proof of the shuffle conjecture},
  year          = {2017},
  month         = may,
  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
  archiveprefix = {arXiv},
  bdsk-url-1    = {https://arxiv.org/abs/1705.11064},
  eprint        = {1705.11064},
  file          = {:Lecture notes on the Carlsson-Mellit proof of the Shuffle Conjecture.pdf:PDF},
  keywords      = {Mathematics - Combinatorics, 05E05, 05E40, 20C08},
  primaryclass  = {math.CO},
  url           = {https://arxiv.org/abs/1705.11064},
}

@InCollection{Haiman1999MacdonaldPolynomialsGeometry,
  author     = {Haiman, Mark},
  booktitle  = {New perspectives in algebraic combinatorics ({B}erkeley, {CA}, 1996--97)},
  publisher  = {Cambridge Univ. Press, Cambridge},
  title      = {Macdonald {P}olynomials and {G}eometry},
  year       = {1999},
  pages      = {207--254},
  series     = {Math. Sci. Res. Inst. Publ.},
  volume     = {38},
  bdsk-url-1 = {http://library.msri.org/books/Book38/files/haiman.pdf},
  file       = {:Macdonald Polynomials and Geometry.pdf:PDF},
  mrclass    = {05E05 (14C05)},
  mrnumber   = {1731818},
  url        = {http://library.msri.org/books/Book38/files/haiman.pdf},
}

@Article{Haiman2001nFactorial,
  author        = {Haiman, Mark},
  journal       = {J. Amer. Math. Soc.},
  title         = {Hilbert schemes, polygraphs and the {M}acdonald positivity conjecture},
  year          = {2001},
  issn          = {0894-0347},
  number        = {4},
  pages         = {941--1006},
  volume        = {14},
  bdsk-url-1    = {https://doi.org/10.1090/S0894-0347-01-00373-3},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Hilbert Schemes, Polygraphs, and the Macdonald Positivity Conjecture.pdf:PDF},
  fjournal      = {Journal of the American Mathematical Society},
  mrclass       = {14C05 (05E05 20C30 33D45)},
  mrnumber      = {1839919},
  mrreviewer    = {Claudio Procesi},
  url           = {https://doi.org/10.1090/S0894-0347-01-00373-3},
}

@Article{Haiman2002HilbertScheme,
  author        = {Haiman, Mark},
  journal       = {Invent Math},
  title         = {Vanishing theorems and character formulas for the {H}ilbert scheme of points in the plane},
  year          = {2002},
  issn          = {0020-9910},
  number        = {2},
  pages         = {371--407},
  volume        = {149},
  bdsk-url-1    = {https://doi.org/10.1007/s002220200219},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Vanishing theorems and character formulas for the Hilbert scheme of points in the plane.pdf:PDF},
  fjournal      = {Inventiones Mathematicae},
  mrclass       = {14C05 (05E05 14F17 14R20)},
  mrnumber      = {1918676},
  mrreviewer    = {Claudio Procesi},
  url           = {https://doi.org/10.1007/s002220200219},
}

@Article{HicksKim2013ExplicitFormulaNdinv,
  author     = {Hicks, Angela and Kim, Yeonkyung},
  journal    = {J. Combin. Theory Ser. A},
  title      = {An explicit formula for ndinv, a new statistic for two-shuffle parking functions},
  year       = {2013},
  issn       = {0097-3165},
  number     = {1},
  pages      = {64--76},
  volume     = {120},
  bdsk-url-1 = {https://doi.org/10.1016/j.jcta.2012.07.006},
  doi        = {10.1016/j.jcta.2012.07.006},
  file       = {:An explicit formula for ndinv, a new statistic for two-shuffle parking functions.pdf:PDF},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {05E05 (05E10)},
  mrnumber   = {2971697},
  mrreviewer = {Matja\v{z} Konvalinka},
  url        = {https://doi.org/10.1016/j.jcta.2012.07.006},
}

 
@Article{HicksSergel2015SimplerFormulaNumber,
  author   = {Hicks, Angela and Sergel, Emily},
  journal  = {Discrete Mathematics},
  title    = {A simpler formula for the number of diagonal inversions of an (m,n)-parking function and a returning fermionic formula},
  year     = {2015},
  issn     = {0012-365X},
  month    = mar,
  number   = {3},
  pages    = {48--65},
  volume   = {338},
  abstract = {Recent results have placed the classical shuffle conjecture of Haglund et al. in a broader context of an infinite family of conjectures about parking functions in any rectangular lattice. The combinatorial side of the new conjectures has been defined using a complicated generalization of the dinv statistic that is composed of three parts and that is not obviously non-negative. Here we simplify the definition of dinv, prove that it is always non-negative, and give a graphical description of the statistic in the style of the classical case. We go on to show that in the (n−1)×n lattice, parking functions satisfy a fermionic formula that is similar to the one given in the classical case by Haglund and Loehr.},
  doi      = {10.1016/j.disc.2014.10.016},
  file     = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/S0012365X14003914/pdfft?md5=178eb140391f5c9994defdcf2a88533a&pid=1-s2.0-S0012365X14003914-main.pdf&isDTMRedir=Y:application/pdf},
  keywords = {Rational parking functions, Shuffle conjecture, Dinv, Diagonal inversions, Fermionic formula},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S0012365X14003914},
  urldate  = {2022-05-17},
}

 
@Article{Hogancamp2017KhovanovRozanskyHomology,
  author   = {Hogancamp, Matthew},
  journal  = {arXiv e-prints},
  title    = {Khovanov-{Rozansky} homology and higher {Catalan} sequences},
  year     = {2017},
  month    = apr,
  note     = {ADS Bibcode: 2017arXiv170401562H Type: article},
  abstract = {We give a simple recursion which computes the triply graded Khovanov-Rozansky homology of several infinite families of knots and links, including the \$(n,nm{\textbackslash}pm 1)\$ and \$(n,nm)\$ torus links for \$n,m{\textbackslash}geq 1\$. We interpret our results in terms of Catalan combinatorics, proving a conjecture of Gorsky's. Our computations agree with predictions coming from Hilbert schemes and rational DAHA, which also proves the Gorsky-Oblomkov-Rasmussen-Shende conjectures in these cases. Additionally, our results suggest a topological interpretation of the symmetric functions which appear in the context of the \$m\$-shuffle conjecture of Haglund-Haiman-Loehr-Remmel-Ulyanov.},
  file     = {:Hogancamp2017 - Khovanov Rozansky Homology and Higher Catalan Sequences.pdf:PDF},
  keywords = {Mathematics - Geometric Topology, Mathematics - Combinatorics, Mathematics - Representation Theory},
  url      = {https://ui.adsabs.harvard.edu/abs/2017arXiv170401562H},
  urldate  = {2022-03-18},
}

 
@Article{IraciRhoadesRomero2023FermionicTheta,
  author   = {Iraci, Alessandro and Rhoades, Brendon and Romero, Marino},
  journal  = {Discrete Mathematics},
  title    = {A proof of the fermionic theta coinvariant conjecture},
  year     = {2023},
  issn     = {0012-365X},
  month    = jul,
  number   = {7},
  pages    = {113474},
  volume   = {346},
  abstract = {Let (x1,…,xn,y1,…,yn) be a list of 2n commuting variables, (θ1,…,θn,ξ1,…,ξn) be a list of 2n anticommuting variables, and C[xn,yn]⊗∧\{θn,ξn\} be the algebra generated by these variables. D'Adderio, Iraci, and Vanden Wyngaerd introduced the Theta operators on the ring of symmetric functions and used them to conjecture a formula for the quadruply-graded Sn-isomorphism type of C[xn,yn]⊗∧\{θn,ξn\}/I where I is the ideal generated by Sn-invariants with vanishing constant term. We prove their conjecture in the ‘purely fermionic setting’ obtained by setting the commuting variables xi,yi equal to zero.},
  doi      = {10.1016/j.disc.2023.113474},
  file     = {:Iraci2023 - A Proof of the Fermionic Theta Coinvariant Conjecture.html:URL},
  keywords = {Symmetric function, Exterior algebra, Coinvariant ring},
  language = {en},
  url      = {https://www.sciencedirect.com/science/article/pii/S0012365X23001607},
  urldate  = {2023-06-29},
}

 
@Article{IraciRomero2022DeltaTheta,
  author        = {{Iraci}, Alessandro and {Romero}, Marino},
  journal       = {arXiv e-prints},
  title         = {{Delta and Theta Operator Expansions}},
  year          = {2022},
  month         = mar,
  pages         = {arXiv:2203.10342},
  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
  adsurl        = {https://ui.adsabs.harvard.edu/abs/2022arXiv220310342I},
  archiveprefix = {arXiv},
  eid           = {arXiv:2203.10342},
  eprint        = {2203.10342},
  keywords      = {Mathematics - Combinatorics, 05E05},
  primaryclass  = {math.CO},
}

@Article{IraciVandenWyngaerd2021Pushing,
  author        = {{Iraci}, Alessandro and {Vanden Wyngaerd}, Anna},
  journal       = {arXiv e-prints},
  title         = {{``Pushing'' our way from the valley Delta to the generalised valley Delta}},
  year          = {2021},
  month         = jan,
  pages         = {arXiv:2101.02600},
  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
  adsurl        = {https://ui.adsabs.harvard.edu/abs/2021arXiv210102600I},
  archiveprefix = {arXiv},
  date-added    = {2021-01-09 10:40:13 +0100},
  date-modified = {2021-01-09 10:40:58 +0100},
  eid           = {arXiv:2101.02600},
  eprint        = {2101.02600},
  keywords      = {Mathematics - Combinatorics},
  primaryclass  = {math.CO},
}

@Article{IraciVandenWyngaerd2021ValleySquare,
  author   = {Iraci, Alessandro and Vanden Wyngaerd, Anna},
  journal  = {Ann Comb},
  title    = {A {Valley} {Version} of the {Delta} {Square} {Conjecture}},
  year     = {2021},
  issn     = {0219-3094},
  month    = mar,
  number   = {1},
  pages    = {195--227},
  volume   = {25},
  abstract = {Inspired by Qiu and Wilson (J Combin Theory Ser A 175:105271, 2020) and D’Adderio et al. (Eur J Combin 81:58–83, 2019), we formulate a generalised Delta square conjecture (valley version). Furthermore, we use similar techniques as in Haglund and Sergel (Schedules and the delta conjecture, arXiv:1908.04732, 2019) to obtain a schedule formula for the combinatorics of our conjecture. We then use this formula to prove that the (generalised) valley version of the Delta conjecture implies our (generalised) valley version of the Delta square conjecture. This implication broadens the argument in Sergel (2016), relying on the formulation of the touching version in terms of the \$\${\textbackslash}varTheta \_f\$\$operators introduced in D’Adderio et al. (Adv Math 107447, 2020).},
  doi      = {10.1007/s00026-021-00525-8},
  language = {en},
  url      = {https://doi.org/10.1007/s00026-021-00525-8},
  urldate  = {2021-07-31},
}

@article{Kasraoui2009,
    AUTHOR = {Kasraoui, Anisse},
     TITLE = {A classification of {M}ahonian maj-inv statistics},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {42},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {342--357},
      ISSN = {0196-8858,1090-2074},
   MRCLASS = {05A05 (05A15 05A30)},
  MRNUMBER = {2502606},
MRREVIEWER = {Astrid\ Reifegerste},
       DOI = {10.1016/j.aam.2008.07.004},
       URL = {https://doi.org/10.1016/j.aam.2008.07.004},
}

 
@TechReport{Kim2022,
  author   = {Kim, Jesse},
  title    = {A combinatorial model for the fermionic diagonal coinvariant ring},
  year     = {2022},
  month    = apr,
  note     = {arXiv:2204.06059 [math] type: article},
  abstract = {Let \${\textbackslash}Theta\_n = ({\textbackslash}theta\_1, {\textbackslash}dots, {\textbackslash}theta\_n)\$ and \${\textbackslash}Xi\_n = ({\textbackslash}xi\_1, {\textbackslash}dots, {\textbackslash}xi\_n)\$ be two lists of \$n\$ variables and consider the diagonal action of \${\textbackslash}mathfrak\{S\}\_n\$ on the exterior algebra \${\textbackslash}wedge {\textbackslash}\{ {\textbackslash}Theta\_n, {\textbackslash}Xi\_n {\textbackslash}\}\$ generated by these variables. Jongwon Kim and Rhoades defined and studied the fermionic diagonal coinvariant ring \$FDR\_n\$ obtained from \${\textbackslash}wedge {\textbackslash}\{ {\textbackslash}Theta\_n, {\textbackslash}Xi\_n {\textbackslash}\}\$ by modding out by the \${\textbackslash}mathfrak\{S\}\_n\$-invariants with vanishing constant term. In joint work with Rhoades we gave a basis for the maximal degree components of this ring where the action of \${\textbackslash}mathfrak\{S\}\_n\$ could be interpreted combinatorially via noncrossing set partitions. This paper will do similarly for the entire ring, although the combinatorial interpretation will be limited to the action of \${\textbackslash}mathfrak\{S\}\_\{n-1\} {\textbackslash}subset {\textbackslash}mathfrak\{S\}\_n\$. The basis will be indexed by a certain class of noncrossing partitions.},
  doi      = {10.48550/arXiv.2204.06059},
  file     = {:Kim2022 - A Combinatorial Model for the Fermionic Diagonal Coinvariant Ring.pdf:PDF},
  keywords = {Mathematics - Combinatorics, Mathematics - Representation Theory, 05E10 (Primary) 05E18, 20C30 (Secondary)},
  school   = {arXiv},
  url      = {http://arxiv.org/abs/2204.06059},
  urldate  = {2023-06-08},
}

@article {KimRhoades2022LefschetzFermionicDiagonal,
    AUTHOR = {Kim, Jongwon and Rhoades, Brendon},
     TITLE = {Lefschetz theory for exterior algebras and fermionic diagonal
              coinvariants},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2022},
    NUMBER = {4},
     PAGES = {2906--2933},
      ISSN = {1073-7928},
   MRCLASS = {20F55 (13D40 16W50)},
  MRNUMBER = {4381935},
       DOI = {10.1093/imrn/rnaa203},
} 

 
@article{KimRhoades2022NoncrossingPartitions,
    author = {Kim, Jesse and Rhoades, Brendon},
    title = "{Set Partitions, Fermions, and Skein Relations}",
    journal = {International Mathematics Research Notices},
    volume = {2023},
    number = {11},
    pages = {9427-9480},
    year = {2022},
    month = {05},
    abstract = "{Let \\$\\Theta \_n = (\\theta \_1, \\dots , \\theta \_n)\\$ and \\$\\Xi \_n = (\\xi \_1, \\dots , \\xi \_n)\\$ be two lists of \\$n\\$ variables, and consider the diagonal action of \\$\\{\\{\\mathfrak \\{S\\}\\}\\}\_n\\$ on the exterior algebra \\$\\wedge \\\\{ \\Theta \_n, \\Xi \_n \\\\}\\$ generated by these variables. Jongwon Kim and the 2nd author defined and studied the fermionic diagonal coinvariant ring\\$FDR\_n\\$ obtained from \\$\\wedge \\\\{ \\Theta \_n, \\Xi \_n \\\\}\\$ by modding out by the ideal generated by the \\$\\{\\{\\mathfrak \\{S\\}\\}\\}\_n\\$-invariants with vanishing constant term. On the other hand, the 2nd author described an action of \\$\\{\\{\\mathfrak \\{S\\}\\}\\}\_n\\$ on the vector space with basis given by noncrossing set partitions of \\$\\\\{1,\\dots ,n\\\\}\\$ using a novel family of skein relations that resolve crossings in set partitions. We give an isomorphism between a natural Catalan-dimensional submodule of \\$FDR\_n\\$ and the skein representation. To do this, we show that set partition skein relations arise naturally in the context of exterior algebras. Our approach yields an \\$\\{\\{\\mathfrak \\{S\\}\\}\\}\_n\\$-equivariant way to resolve crossings in set partitions. We use fermions to clarify, sharpen, and extend the theory of set partition crossing resolution.}",
    issn = {1073-7928},
    doi = {10.1093/imrn/rnac110},
    url = {https://doi.org/10.1093/imrn/rnac110},
}

@Article{Kreweras1980,
  author   = {Kreweras, Germain},
  journal  = {Periodica Mathematica Hungarica},
  title    = {Une famille de polynômes ayant plusieurs propriétés énumeratives},
  year     = {1980},
  issn     = {1588-2829},
  month    = dec,
  number   = {4},
  pages    = {309--320},
  volume   = {11},
  doi      = {10.1007/BF02107572},
  language = {fr},
  url      = {https://doi.org/10.1007/BF02107572},
  urldate  = {2021-10-16},
}

@Article{LascouxLeclercThibon1997LLTs,
  author    = {Lascoux, Alain and Leclerc, Bernard and Thibon, Jean-Yves},
  journal   = {Journal of Mathematical Physics},
  title     = {Ribbon tableaux, {Hall}–{Littlewood} functions, quantum affine algebras, and unipotent varieties},
  year      = {1997},
  issn      = {0022-2488},
  month     = feb,
  number    = {2},
  pages     = {1041--1068},
  volume    = {38},
  doi       = {10.1063/1.531807},
  file      = {:Lascoux1997 - Ribbon Tableaux, Hall–Littlewood Functions, Quantum Affine Algebras, and Unipotent Varieties.html:URL},
  publisher = {American Institute of Physics},
  url       = {https://aip.scitation.org/doi/10.1063/1.531807},
  urldate   = {2022-03-17},
}

@Article{Loehr2005ParkingFunctions,
  author        = {Loehr, Nicholas A.},
  journal       = {Adv Appl Math},
  title         = {Combinatorics of {$q,t$}-parking functions},
  year          = {2005},
  issn          = {0196-8858},
  number        = {2},
  pages         = {408--425},
  volume        = {34},
  bdsk-url-1    = {https://doi.org/10.1016/j.aam.2004.08.002},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Combinatorics of q,t-parking functions.pdf:PDF},
  fjournal      = {Advances in Applied Mathematics},
  mrclass       = {05A30 (05A15)},
  mrnumber      = {2110560},
  mrreviewer    = {Catherine H. Yan},
  url           = {https://doi.org/10.1016/j.aam.2004.08.002},
}

@Book{Loehr2011Book,
  author     = {Loehr, Nicholas A.},
  publisher  = {CRC Press, Boca Raton, FL},
  title      = {Bijective combinatorics},
  year       = {2011},
  isbn       = {978-1-4398-4884-5},
  series     = {Discrete Mathematics and its Applications (Boca Raton)},
  file       = {:Bijective Combinatorics.pdf:PDF},
  mrclass    = {05-01 (05A15 05A19 05E05 05E10 05E18)},
  mrnumber   = {2777360},
  mrreviewer = {David Callan},
  pages      = {xxii+590},
}

@Article{LoehrRemmel2004HilbertSeriesHarmonics,
  author        = {Loehr, Nicholas A. and Remmel, Jeffrey B.},
  journal       = {Electron J Comb},
  title         = {Conjectured combinatorial models for the {H}ilbert series of generalized diagonal harmonics modules},
  year          = {2004},
  issn          = {1077-8926},
  number        = {1},
  pages         = {Research Paper 68, 64},
  volume        = {11},
  bdsk-url-1    = {http://www.combinatorics.org/Volume_11/Abstracts/v11i1r68.html},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Conjectured combinatorial models for the Hilbert series of generalized diagonal harmonics modules.pdf:PDF},
  fjournal      = {Electronic Journal of Combinatorics},
  mrclass       = {05E05 (05A10 11B65 20C30)},
  mrnumber      = {2097334},
  mrreviewer    = {Eric S. Egge},
  url           = {http://www.combinatorics.org/Volume_11/Abstracts/v11i1r68.html},
}

@Article{LoehrRemmel2011ExposePlethystic,
  author        = {Loehr, Nicholas A. and Remmel, Jeffrey B.},
  journal       = {J Algebr Comb},
  title         = {A computational and combinatorial expos\'e of plethystic calculus},
  year          = {2011},
  issn          = {0925-9899},
  number        = {2},
  pages         = {163--198},
  volume        = {33},
  bdsk-url-1    = {https://doi.org/10.1007/s10801-010-0238-4},
  date-added    = {2018-01-24 16:28:21 +0000},
  date-modified = {2018-01-24 16:28:56 +0000},
  file          = {:A computational and combinatorial expos{\'e} of plethystic calculus.pdf:PDF},
  fjournal      = {Journal of Algebraic Combinatorics. An International Journal},
  mrclass       = {05E05},
  mrnumber      = {2765321},
  mrreviewer    = {Kurt W. Luoto},
  url           = {https://doi.org/10.1007/s10801-010-0238-4},
}

@Article{LoehrWarrington2007Square,
  author        = {Loehr, Nicholas A. and Warrington, Gregory S.},
  journal       = {Trans. Amer. Math. Soc.},
  title         = {Square {$q,t$}-lattice paths and {$\nabla(p_n)$}},
  year          = {2007},
  issn          = {0002-9947},
  number        = {2},
  pages         = {649--669},
  volume        = {359},
  bdsk-url-1    = {https://doi.org/10.1090/S0002-9947-06-04044-X},
  date-added    = {2018-01-24 15:53:30 +0000},
  date-modified = {2018-01-24 15:54:02 +0000},
  file          = {:Square q,t-lattice paths and ∇(p_n).pdf:PDF},
  fjournal      = {Transactions of the American Mathematical Society},
  mrclass       = {05E10 (20C30)},
  mrnumber      = {2255191},
  mrreviewer    = {Kendra Killpatrick},
  url           = {https://doi.org/10.1090/S0002-9947-06-04044-X},
}

@Article{Lopez1997ChipFiring,
  author   = {López, Criel Merino},
  journal  = {Annals of Combinatorics},
  title    = {Chip firing and the tutte polynomial},
  year     = {1997},
  issn     = {0219-3094},
  month    = dec,
  number   = {1},
  pages    = {253--259},
  volume   = {1},
  abstract = {It is shown that the generating function of critical configurations of a version of a chip firing game on a graphG is an evaluation of the Tutte polynomial ofG, thus proving a conjecture of Biggs [3].},
  doi      = {10.1007/BF02558479},
  file     = {:Lopez1997 - Chip Firing and the Tutte Polynomial/Lopez1997 - Chip Firing and the Tutte Polynomial.pdf:PDF},
  language = {en},
  url      = {https://doi.org/10.1007/BF02558479},
  urldate  = {2021-11-03},
}

@article{Lothaire1997,
    AUTHOR = {Lothaire, M.},
     TITLE = {Combinatorics on words},
    SERIES = {Cambridge Mathematical Library},
      NOTE = {With a foreword by Roger Lyndon and a preface by Dominique
              Perrin,
              Corrected reprint of the 1983 original, with, a new preface by
              Perrin},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1997},
     PAGES = {xviii+238},
      ISBN = {0-521-59924-5},
   MRCLASS = {68R15 (03D03 03D40 05A99 20M05)},
  MRNUMBER = {1475463},
       DOI = {10.1017/CBO9780511566097},
       URL = {https://doi.org/10.1017/CBO9780511566097},
}

@Article{Macdonald1988,
  author        = {Macdonald, Ian},
  journal       = {Sem. Lothar. Combin.},
  title         = {A new class of symmetric functions},
  year          = {1988},
  pages         = {B20a, 41 p.-B20a, 41 p.},
  volume        = {20},
  bdsk-url-1    = {http://eudml.org/doc/120965},
  date-added    = {2021-01-08 15:25:49 +0100},
  date-modified = {2021-01-08 15:25:49 +0100},
  keywords      = {Jack symmetric functions; Schur functions; Hall-Littlewood functions},
  language      = {eng},
  publisher     = {Universit{\"a}t Wien, Fakult{\"a}t f{\"u}r Mathematik},
  url           = {http://eudml.org/doc/120965},
}

@Book{Macdonald1995Book,
  author        = {Macdonald, Ian G.},
  publisher     = {The Clarendon Press, Oxford University Press, New York},
  title         = {Symmetric functions and {H}all polynomials},
  year          = {1995},
  edition       = {Second},
  isbn          = {0-19-853489-2},
  note          = {With contributions by A. Zelevinsky, Oxford Science Publications},
  series        = {Oxford Mathematical Monographs},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Symmetric Functions and Hall Polynomials.pdf:PDF},
  mrclass       = {05E05 (05-02 20C30 20C33 20K01 33C80 33D80)},
  mrnumber      = {1354144},
  mrreviewer    = {John R. Stembridge},
  pages         = {x+475},
}

 
@Article{Mellit2017HomologyTorusKnots,
  author   = {Mellit, Anton},
  journal  = {arXiv:1704.07630 [math]},
  title    = {Homology of torus knots},
  year     = {2017},
  month    = apr,
  note     = {arXiv: 1704.07630},
  abstract = {Using the method of Elias-Hogancamp and combinatorics of toric braids we give an explicit formula for the triply graded Khovanov-Rozansky homology of an arbitrary torus knot, thereby proving some of the conjectures of Aganagic-Shakirov, Cherednik, Gorsky-Negut and Oblomkov-Rasmussen-Shende.},
  file     = {:Mellit2017 - Homology of Torus Knots.pdf:PDF},
  keywords = {Mathematics - Quantum Algebra, Mathematics - Algebraic Geometry, Mathematics - Geometric Topology, Mathematics - Representation Theory},
  url      = {http://arxiv.org/abs/1704.07630},
  urldate  = {2022-03-17},
}

@Article{Mellit2020SpringerFibers,
  author    = {Mellit, Anton},
  journal   = {Annals of Mathematics},
  title     = {Poincaré polynomials of character varieties, {Macdonald} polynomials and affine {Springer} fibers},
  year      = {2020},
  issn      = {0003-486X, 1939-8980},
  month     = jul,
  number    = {1},
  pages     = {165--228},
  volume    = {192},
  abstract  = {We prove an explicit formula for the Poincaré polynomials of parabolic character varieties of Riemann surfaces with semisimple local monodromies, which was conjectured by Hausel, Letellier and Rodriguez-Villegas. Using an approach of Mozgovoy and Schiffmann the problem is reduced to counting pairs of a parabolic vector bundle and a nilpotent endomorphism of prescribed generic type. The generating function counting these pairs is shown to be a product of Macdonald polynomials and the function counting pairs without parabolic structure. The modified Macdonald polynomial \${\textbackslash}tilde H\_{\textbackslash}lambda [X;q,t]\$ is interpreted as a weighted count of points of the affine Springer fiber over the constant nilpotent matrix of type \${\textbackslash}lambda\$.},
  doi       = {10.4007/annals.2020.192.1.3},
  file      = {:Mellit2020 - Poincaré Polynomials of Character Varieties, Macdonald Polynomials and Affine Springer Fibers.html:URL},
  keywords  = {14H60, Character varieties, Hall algebras, Higgs bundles, Macdonald polynomials, Poincaré polynomials},
  publisher = {Department of Mathematics of Princeton University},
  url       = {https://projecteuclid.org/journals/annals-of-mathematics/volume-192/issue-1/Poincaré-polynomials-of-character-varieties-Macdonald-polynomials-and-affine-Springer/10.4007/annals.2020.192.1.3.full},
  urldate   = {2022-01-31},
}

@Article{Mellit2021Rational,
  author    = {Mellit, Anton},
  journal   = {Duke Mathematical Journal},
  title     = {Toric braids and (m,n)-parking functions},
  year      = {2021},
  issn      = {0012-7094, 1547-7398},
  month     = {dec},
  number    = {18},
  pages     = {4123--4169},
  volume    = {170},
  abstract  = {We find a geometric interpretation of the Aq,t algebra, the algebra which appeared in the previous work of Erik Carlsson and the author on the proof of the shuffle conjecture. This allows us to construct a representation of “the positive part” of the group of toric braids. Then certain sums over (m,n)-parking functions are related to evaluations of this representation on some special braids. The compositional (km,kn)-shuffle conjecture of Bergeron, Garsia, Leven, and Xin is then shown to be a corollary of this relation.},
  doi       = {10.1215/00127094-2021-0011},
  file      = {:Mellit2021 - Toric Braids and (m,n) Parking Functions.html:URL},
  keywords  = {05A15, 05E05, 20C08, 20F36, Dyck paths, parking functions, shuffle conjecture, symmetric functions, toric braids},
  publisher = {Duke University Press},
  url       = {https://projecteuclid.org/journals/duke-mathematical-journal/volume-170/issue-18/Toric-braids-and-mn-parking-functions/10.1215/00127094-2021-0011.full},
  urldate   = {2022-03-17},
}

@Article{PerkinsonYangYu2017GParkingFunctions,
  author   = {Perkinson, David and Yang, Qiaoyu and Yu, Kuai},
  journal  = {Combinatorica},
  title    = {G-parking functions and tree inversions},
  year     = {2017},
  issn     = {1439-6912},
  month    = apr,
  number   = {2},
  pages    = {269--282},
  volume   = {37},
  abstract = {A depth-first search version of Dhar’s burning algorithm is used to give a bijection between the parking functions of a graph and labeled spanning trees, relating the degree of the parking function with the number of inversions of the spanning tree. Specializing to the complete graph solves a problem posed by R. Stanley.},
  doi      = {10.1007/s00493-015-3191-y},
  language = {en},
  url      = {https://doi.org/10.1007/s00493-015-3191-y},
  urldate  = {2021-09-15},
}

@Article{Postnikov1997IntransitiveTrees,
  author   = {Alexander Postnikov},
  journal  = {J. Combin. Theory Ser. A},
  title    = {Intransitive {T}rees},
  year     = {1997},
  issn     = {0097-3165},
  number   = {2},
  pages    = {360-366},
  volume   = {79},
  abstract = {We study the class of treesTon the set {1, 2, …, n} such that for any 1⩽i<j<k⩽nthe pairs {i, j} and {j, k} cannot both be edges inT. We derive a formula for the number of such trees. We also give a functional equation and a differential equation for the generating function. We mention some additional combinatorial interpretations of these numbers.},
  doi      = {https://doi.org/10.1006/jcta.1996.2735},
  url      = {https://www.sciencedirect.com/science/article/pii/S0097316596927351},
}

@Article{QiuRemmelSergelXin2018SchurPositivity,
  author     = {Qiu, Dun and Remmel, Jeffrey B. and Sergel, Emily and Xin, Guoce},
  journal    = {Electron J Comb},
  title      = {On the {S}chur positivity of {$\Delta_{e_2}e_n[X]$}},
  year       = {2018},
  issn       = {1077-8926},
  number     = {4},
  pages      = {Paper 4.20, 27},
  volume     = {25},
  bdsk-url-1 = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p20/pdf},
  file       = {:On the Schur Positivity of Delta_e2 en[X].pdf:PDF},
  fjournal   = {Electronic Journal of Combinatorics},
  mrclass    = {05E05 (05E10)},
  mrnumber   = {3874286},
  mrreviewer = {Lucas Fresse},
  url        = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p20/pdf},
}

@Article{QiuWilson2020ValleyExtendedDelta,
  author     = {Dun Qiu and Andrew Timothy Wilson},
  journal    = {J. Combin. Theory Ser. A},
  title      = {The valley version of the {E}xtended {D}elta {C}onjecture},
  year       = {2020},
  issn       = {0097-3165},
  pages      = {105271},
  volume     = {175},
  abstract   = {The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression for the bigraded Frobenius characteristic of the ring of diagonal harmonics, and the Delta Conjecture of Haglund, Remmel and the second author provides two generalizations of the Shuffle Theorem to the delta operator expression Δek′en. Haglund et al. also propose the Extended Delta Conjecture for the delta operator expression Δek′Δhren, which is analogous to the rise version of the Delta Conjecture. Recently, D'Adderio, Iraci and Wyngaerd proved the rise version of the Extended Delta Conjecture at the case when t=0. In this paper, we propose a new valley version of the Extended Delta Conjecture. Then, we work on the combinatorics of extended ordered multiset partitions to prove that the two conjectures for Δek′Δhren are equivalent when t or q equals 0, thus proving the valley version of the Extended Delta Conjecture when t or q equals 0.},
  bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0097316520300637},
  bdsk-url-2 = {https://doi.org/10.1016/j.jcta.2020.105271},
  doi        = {https://doi.org/10.1016/j.jcta.2020.105271},
  keywords   = {Macdonald polynomials, Symmetric functions, Parking functions, Ordered set partitions},
  url        = {http://www.sciencedirect.com/science/article/pii/S0097316520300637},
}

@Article{RemmelWilson2015ExtensionMacmahonsEquidistribution,
  author     = {Remmel, Jeffrey B. and Wilson, Andrew T.},
  journal    = {J. Combin. Theory Ser. A},
  title      = {An extension of {M}ac{M}ahon's equidistribution theorem to ordered set partitions},
  year       = {2015},
  issn       = {0097-3165},
  pages      = {242--277},
  volume     = {134},
  bdsk-url-1 = {https://doi.org/10.1016/j.jcta.2015.03.012},
  doi        = {10.1016/j.jcta.2015.03.012},
  file       = {:An extension of MacMahon's equidistribution theorem to ordered set partitions.pdf:PDF},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {05A18 (05A15)},
  mrnumber   = {3345306},
  mrreviewer = {Damir Yeliussizov},
  url        = {https://doi.org/10.1016/j.jcta.2015.03.012},
}

@Article{Rhoades2018OrderedSetPartition,
  author     = {Rhoades, Brendon},
  journal    = {J. Combin. Theory Ser. A},
  title      = {Ordered set partition statistics and the {D}elta {C}onjecture},
  year       = {2018},
  issn       = {0097-3165},
  pages      = {172--217},
  volume     = {154},
  bdsk-url-1 = {https://doi.org/10.1016/j.jcta.2017.08.017},
  doi        = {10.1016/j.jcta.2017.08.017},
  file       = {:Ordered set partitions statistics and the Delta Conjecture.pdf:PDF},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {05E05 (05A05 05A18)},
  mrnumber   = {3718065},
  url        = {https://doi.org/10.1016/j.jcta.2017.08.017},
}

@Article{RhoadesWilson2020VandermondesSuperspace,
  author        = {Rhoades, Brendon and Wilson, Andrew},
  journal       = {Trans. Amer. Math. Soc.},
  title         = {Vandermondes in superspace},
  year          = {2020},
  date-added    = {2021-01-06 16:09:01 +0100},
  date-modified = {2021-01-06 16:09:01 +0100},
}
  
@Article{RhoadesWilson2023Superspace,
  author        = {{Rhoades}, Brendon and {Wilson}, Andy},
  title         = {{The Hilbert series of the superspace coinvariant ring}},
  year          = {2023},
  month         = jan,
  adsnote       = {Provided by the SAO/NASA Astrophysics Data System},
  adsurl        = {https://ui.adsabs.harvard.edu/abs/2023arXiv230109763R},
  archiveprefix = {arXiv},
  eprint        = {2301.09763},
  keywords      = {Mathematics - Combinatorics},
  primaryclass  = {math.CO},
}

@Article{RhoadesYuZhao2020HarmonicBases,
  author        = {Rhoades, Brendon and Yu, Tianyi and Zhao, Zehong},
  journal       = {ArXiv e-prints},
  title         = {Harmonic bases for generalized coinvariant algebras},
  year          = {2020},
  date-added    = {2021-01-06 16:09:13 +0100},
  date-modified = {2021-01-06 16:09:13 +0100},
}

@Article{Romero2017Deltaq1,
  author        = {Romero, Marino},
  journal       = {Trans. Amer. Math. Soc.},
  title         = {The {D}elta conjecture at {$q=1$}},
  year          = {2017},
  issn          = {0002-9947},
  number        = {10},
  pages         = {7509--7530},
  volume        = {369},
  bdsk-url-1    = {https://doi.org/10.1090/tran/7140},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:The Delta Conjecture at q=1.pdf:PDF},
  fjournal      = {Transactions of the American Mathematical Society},
  mrclass       = {05E05 (05E10)},
  mrnumber      = {3683116},
  url           = {https://doi.org/10.1090/tran/7140},
}

@article {Rosas2001KroneckerHook,
    AUTHOR = {Rosas, Mercedes H.},
     TITLE = {The {K}ronecker product of {S}chur functions indexed by
              two-row shapes or hook shapes},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {14},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {153--173},
      ISSN = {0925-9899},
   MRCLASS = {05E05},
  MRNUMBER = {1867232},
MRREVIEWER = {Grant Walker},
       DOI = {10.1023/A:1011942029902},
       URL = {https://doi-org.docelec.univ-lyon1.fr/10.1023/A:1011942029902},
}

@Article{Sergel2017SquarePaths,
  author     = {Sergel, Emily},
  journal    = {J. Combin. Theory Ser. A},
  title      = {A proof of the {S}quare {P}aths {C}onjecture},
  year       = {2017},
  issn       = {0097-3165},
  pages      = {363--379},
  volume     = {152},
  bdsk-url-1 = {https://doi.org/10.1016/j.jcta.2017.06.013},
  doi        = {10.1016/j.jcta.2017.06.013},
  file       = {:A proof of the Square Paths Conjecture.pdf:PDF},
  fjournal   = {Journal of Combinatorial Theory. Series A},
  mrclass    = {05E05 (05E15)},
  mrnumber   = {3682738},
  mrreviewer = {Edward E. Allen},
  url        = {https://doi.org/10.1016/j.jcta.2017.06.013},
}

@article {ShareshianWachs2016Chromatic,
    AUTHOR = {Shareshian, John and Wachs, Michelle L.},
     TITLE = {Chromatic quasisymmetric functions},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {295},
      YEAR = {2016},
     PAGES = {497--551},
      ISSN = {0001-8708},
   MRCLASS = {05E05 (14M15)},
  MRNUMBER = {3488041},
MRREVIEWER = {Meesue Yoo},
       DOI = {10.1016/j.aim.2015.12.018},
       URL = {https://doi-org.docelec.univ-lyon1.fr/10.1016/j.aim.2015.12.018},
}

@incollection{ShareshianWachs2012ChromaticHessenberg,
    AUTHOR = {Shareshian, John and Wachs, Michelle L.},
     TITLE = {Chromatic quasisymmetric functions and {H}essenberg varieties},
 BOOKTITLE = {Configuration spaces},
    SERIES = {CRM Series},
    VOLUME = {14},
     PAGES = {433--460},
 PUBLISHER = {Ed. Norm., Pisa},
      YEAR = {2012},
      ISBN = {978-88-7642-430-4; 978-88-7642-431-1},
   MRCLASS = {05E05 (14M25)},
  MRNUMBER = {3203651},
       DOI = {10.1007/978-88-7642-431-1\_20},
}

@Book{Stanley1999EnumerativeCombinatoricsV2,
  author        = {Stanley, Richard P.},
  publisher     = {Cambridge University Press, Cambridge},
  title         = {Enumerative combinatorics {V}ol. 2},
  year          = {1999},
  isbn          = {0-521-56069-1; 0-521-78987-7},
  note          = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin},
  series        = {Cambridge Studies in Advanced Mathematics},
  volume        = {62},
  bdsk-url-1    = {https://doi.org/10.1017/CBO9780511609589},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Enumerative combinatorics (vol.2) - Stanley, Richard.pdf:PDF},
  mrclass       = {05A15 (05-02 05E05 05E10 68R05)},
  mrnumber      = {1676282},
  mrreviewer    = {Ira Gessel},
  pages         = {xii+581},
  url           = {https://doi.org/10.1017/CBO9780511609589},
}

@Book{Stanley2015CatalanNumbers,
  author     = {Stanley, Richard P.},
  publisher  = {Cambridge University Press},
  title      = {Catalan {N}umbers},
  year       = {2015},
  bdsk-url-1 = {https://doi.org/10.1017/CBO9781139871495},
  doi        = {10.1017/CBO9781139871495},
  file       = {:Catalan Numbers.pdf:PDF},
  place      = {Cambridge},
}

 
@Article{Steingrimsson2020,
  author    = {Steingrímsson, Einar},
  journal   = {Journal of Combinatorics},
  title     = {Statistics on ordered partitions of sets},
  year      = {2020},
  issn      = {2150-959X},
  number    = {3},
  pages     = {557--574},
  volume    = {11},
  abstract  = {International Press of Boston - publishers of scholarly mathematical and scientific journals and books},
  doi       = {10.4310/JOC.2020.v11.n3.a8},
  file      = {Full Text PDF:https\://www.intlpress.com/site/pub/files/_fulltext/journals/joc/2020/0011/0003/JOC-2020-0011-0003-a008.pdf:application/pdf},
  language  = {EN},
  publisher = {International Press of Boston},
  url       = {https://www.intlpress.com/site/pub/pages/journals/items/joc/content/vols/0011/0003/a008/abstract.php},
  urldate   = {2023-06-08},
}

@Article{Tutte1954ChromaticPolynomials,
  author    = {Tutte, William T.},
  journal   = {Canadian Journal of Mathematics},
  title     = {A {Contribution} to the {Theory} of {Chromatic} {Polynomials}},
  year      = {1954},
  issn      = {0008-414X, 1496-4279},
  pages     = {80--91},
  volume    = {6},
  abstract  = {Two polynomials ?(G, n) and ?(G, n) connected with the colourings of a graph G or of associated maps are discussed. A result believed to be new is proved for the lesser-known polynomial ?(G, n). Attention is called to some unsolved problems concerning ?(G, n) which are natural generalizations of the Four Colour Problem from planar graphs to general graphs. A polynomial ?(G, x, y) in two variables x and y, which can be regarded as generalizing both ?(G, n) and ?(G, n) is studied. For a connected graph ?(G, x, y) is defined in terms of the “spanning” trees of G (which include every vertex) and in terms of a fixed enumeration of the edges.},
  doi       = {10.4153/CJM-1954-010-9},
  file      = {Full Text PDF:https\://www.cambridge.org/core/services/aop-cambridge-core/content/view/E1EE1F053B494D08746F0EE23F736CC2/S0008414X00023543a.pdf/div-class-title-a-contribution-to-the-theory-of-chromatic-polynomials-div.pdf:application/pdf},
  language  = {en},
  publisher = {Cambridge University Press},
  url       = {https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/contribution-to-the-theory-of-chromatic-polynomials/E1EE1F053B494D08746F0EE23F736CC2},
  urldate   = {2021-09-15},
}

@Book{Wilson2015PhDThesis,
  author        = {Wilson, Andrew T.},
  publisher     = {ProQuest LLC, Ann Arbor, MI},
  title         = {Generalized {S}huffle {C}onjectures for the {G}arsia-{H}aiman {D}elta {O}perator},
  year          = {2015},
  isbn          = {978-1321-85316-2},
  note          = {Thesis (Ph.D.)--University of California, San Diego},
  bdsk-url-1    = {http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:3709671},
  date-added    = {2018-01-23 11:09:38 +0000},
  date-modified = {2018-01-23 11:09:38 +0000},
  file          = {:Generalized Shuffle Conjectures for the Garsia-Haiman Delta Operator.pdf:PDF},
  mrclass       = {Thesis},
  mrnumber      = {3407349},
  pages         = {157},
  url           = {https://search.proquest.com/docview/1699058784},
}

@Article{Wilson2016Equidistribution,
  author     = {Wilson, Andrew T.},
  journal    = {Electron J Comb},
  title      = {An extension of {M}ac{M}ahon's equidistribution theorem to ordered multiset partitions},
  year       = {2016},
  issn       = {1077-8926},
  number     = {1},
  pages      = {Paper 1.5, 21},
  volume     = {23},
  bdsk-url-1 = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p5/pdf},
  file       = {:An extension of MacMahon's equidistribution theorem to ordered multiset partitions.pdf:PDF},
  fjournal   = {Electronic Journal of Combinatorics},
  mrclass    = {05A19 (05A05 05A18 05E05)},
  mrnumber   = {3484710},
  mrreviewer = {Zhicong Lin},
  url        = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i1p5/pdf},
}

@Article{Wilson2017TeslerMatrices,
  author     = {Wilson, Andrew T.},
  journal    = {J Algebr Comb},
  title      = {A weighted sum over generalized {T}esler matrices},
  year       = {2017},
  issn       = {0925-9899},
  number     = {3},
  pages      = {825--855},
  volume     = {45},
  bdsk-url-1 = {https://doi.org/10.1007/s10801-016-0726-2},
  doi        = {10.1007/s10801-016-0726-2},
  file       = {:A weighted sum over generalized Tesler matrices.pdf:PDF},
  fjournal   = {Journal of Algebraic Combinatorics. An International Journal},
  mrclass    = {05E05 (33D52)},
  mrnumber   = {3627505},
  mrreviewer = {Markus E. Fulmek},
  url        = {https://doi.org/10.1007/s10801-016-0726-2},
}

@Article{XinZhang2020DinvAreaBounce,
  author     = {Xin, Guoce and Zhang, Yingrui},
  title      = {Dinv, {Area}, and {Bounce} for \${\textbackslash}vec\{k\}\$-{Dyck} paths},
  year       = {2020},
  month      = nov,
  note       = {arXiv: 2011.04927},
  bdsk-url-1 = {http://arxiv.org/abs/2011.04927},
  file       = {arXiv Fulltext PDF:https\://arxiv.org/pdf/2011.04927.pdf:application/pdf},
  keywords   = {Mathematics - Combinatorics},
  url        = {http://arxiv.org/abs/2011.04927},
  urldate    = {2020-11-11},
}

@Article{Zabrocki2019ModuleDeltaConjecture,
  author        = {Zabrocki, Mike},
  title         = {A module for the {D}elta conjecture},
  year          = {2019},
  month         = {Feb},
  archiveprefix = {arXiv},
  eprint        = {1902.08966},
  file          = {:A module for the Delta conjecture.pdf:PDF},
  keywords      = {Mathematics - Combinatorics, 05E05, 05E10, 20C30},
  primaryclass  = {math.CO},
}

 
@Article{Zabrocki2019Proof4Catalan,
  author    = {Zabrocki, Mike},
  journal   = {Journal of Combinatorics},
  title     = {A proof of the 4-variable {Catalan} polynomial of the {Delta} conjecture},
  year      = {2019},
  issn      = {2150-959X},
  number    = {4},
  pages     = {599--632},
  volume    = {10},
  abstract  = {International Press of Boston - publishers of scholarly mathematical and scientific journals and books},
  doi       = {10.4310/JOC.2019.v10.n4.a1},
  language  = {EN},
  publisher = {International Press of Boston},
  url       = {https://www.intlpress.com/site/pub/pages/journals/items/joc/content/vols/0010/0004/a001/abstract.php},
  urldate   = {2022-10-15},
}

@Comment{jabref-meta: databaseType:bibtex;}

@Comment{jabref-meta: saveOrderConfig:specified;citationkey;false;author;false;title;true;}