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@article{LascouxSchutzenberger-SchubertLittlewoudRichardson,
	Author = {Lascoux, Alain and Sch\"utzenberger, Marcel-Paul},
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@article{LascouxSchutzenberger-PolynomesSchubert,
	Author = {Lascoux, Alain and Sch\"utzenberger, Marcel-Paul},
	Fjournal = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique},
	Journal = {C. R. Math. Acad. Sci. Paris},
	Number = {13},
	Pages = {447--450},
	Title = {Polyn\^omes de {Schubert}},
	Volume = {294},
	Year = {1982}}

@article{ArmstrongLoehrWarrington-parking,
	Author = {Armstrong, Drew and Loehr, Nicholas A. and Warrington, Gregory S.},
	Fjournal = {Annals of Combinatorics},
	Journal = {Ann. Comb.},
	Number = {1},
	Pages = {21--58},
	Title = {Rational Parking Functions and {Catalan} Numbers},
	Volume = {20},
	Year = {2015}}

@article{ArmstrongLoehrWarrington-sweep,
	Author = {Armstrong, Drew and Loehr, Nicholas A. and Warrington, Gregory S.},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Pages = {159--185},
	Title = {Sweep maps: a continuous family of sorting algorithms},
	Volume = {284},
	Year = {2015}}

@article{Bergeron-rectangular,
	Author = {Bergeron, Fran\c{c}ois},
	Fjournal = {Journal of Combinatorics},
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	Number = {4},
	Pages = {673--703},
	Title = {Open questions for operators related to rectangular {C}atalan combinatorics},
	Volume = {8},
	Year = {2017}}

@article{BergeronGarsiaSergelLevenXin-compositional,
	Author = {Bergeron, Francois and Garsia, Adriano and Sergel Leven, Emily and Xin, Guoce},
	Fjournal = {International Mathematics Research Notices. IMRN},
	Journal = {Int. Math. Res. Not. IMRN},
	Pages = {4229--4270},
	Title = {Compositional {$(km,kn)$}-shuffle conjectures},
	Volume = {14},
	Year = {2016}}

@unpublished{Mellit-rationalshuffle,
	Author = {Mellit, Anton},
	Note = {Preprint, \href{https://arxiv.org/abs/1604.07456}{\texttt{arXiv:1604.07456}}},
	Title = {Toric braids and $(m,n)$-parking functions},
	Year = {2016}}

@unpublished{Mellit-homology,
	Author = {Mellit, Anton},
	Note = {Preprint, \href{https://arxiv.org/abs/1704.07630}{\texttt{arXiv:1704.07630}}},
	Title = {Homology of torus knots},
	Year = {2017}}

@article{bergeron_identities_1999,
	Author = {Bergeron, Fran\c{c}ois and Garsia, Adriano M. and Haiman, Mark and Tesler, Glenn},
	Doi = {10.4310/MAA.1999.v6.n3.a7},
	Issn = {1945-0001},
	Journal = {Methods and Applications of Analysis},
	Month = sep,
	Number = {3},
	Pages = {363--420},
	Title = {Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions},
	Url = {http://intlpress.com/site/pub/pages/journals/items/maa/content/vols/0006/0003/a007/index.html},
	Urldate = {2017-08-24},
	Volume = {6},
	Year = {1999},
	Bdsk-Url-1 = {http://intlpress.com/site/pub/pages/journals/items/maa/content/vols/0006/0003/a007/index.html},
	Bdsk-Url-2 = {https://doi.org/10.4310/MAA.1999.v6.n3.a7}}

@article{garsia_proof_2002,
	Author = {Garsia, Adriano M. and Haglund, James},
	Doi = {10.1016/S0012-365X(02)00343-6},
	Issn = {0012-365X},
	Journal = {Discrete Mathematics},
	Month = oct,
	Number = {3},
	Pages = {677--717},
	Series = {{LaCIM} 2000 {Conference} on {Combinatorics}, {Computer} {Science} and {Applications}},
	Title = {A proof of the q,t-{Catalan} positivity conjecture},
	Url = {http://www.sciencedirect.com/science/article/pii/S0012365X02003436},
	Urldate = {2017-08-24},
	Volume = {256},
	Year = {2002},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0012365X02003436},
	Bdsk-Url-2 = {https://doi.org/10.1016/S0012-365X(02)00343-6}}

@article{haglund_conjectured_2003,
	Author = {Haglund, J.},
	Doi = {10.1016/S0001-8708(02)00061-0},
	Issn = {0001-8708},
	Journal = {Advances in Mathematics},
	Keywords = {Catalan words, Lagrange inversion, Major index statistic},
	Month = may,
	Number = {2},
	Pages = {319--334},
	Title = {Conjectured statistics for the $q,t$-{Catalan} numbers},
	Url = {http://www.sciencedirect.com/science/article/pii/S0001870802000610},
	Urldate = {2016-10-25},
	Volume = {175},
	Year = {2003},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0001870802000610},
	Bdsk-Url-2 = {https://doi.org/10.1016/S0001-8708(02)00061-0}}

@inproceedings{Macdonald-newClassSymFunct,
	Author = {Macdonald, Ian G.},
	Booktitle = {Publ. {I}.{R}.{M}.{A}. {Strasbourg}, 372/{S}20, {Actes} 20 {S}\'eminaire {Lotharingien}},
	Pages = {131--171},
	Title = {A New Class Of Symmetric Functions},
	Year = {1988}}

@article{LapointeVinet,
	Author = {Lapointe, Luc and Vinet, Luc},
	Fjournal = {Letters in Mathematical Physics},
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	Pages = {269--286},
	Title = {Creation {Operators} for the {Macdonald} and {Jack} {Polynomials}},
	Volume = {40},
	Year = {1997}}

@article{Macconald-affineHeckeAlgebras,
	Author = {Macdonald, Ian G.},
	Journal = {S\'eminaire Bourbaki},
	Pages = {189--207},
	Title = {Affine {Hecke} algebras and orthogonal polynomials},
	Volume = {37},
	Year = {1994}}

@article{Knop,
	Author = {Knop, Friedrich},
	Fjournal = {Journal f\"ur die Reine und Angewandte Mathematik},
	Journal = {J. Reine Angew. Math.},
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	Title = {Integrality of two variable {Kostka} functions},
	Volume = {482},
	Year = {1997}}

@article{DalalMorse,
	Author = {Dalal, Avinash J. and Morse, Jennifer},
	Fjournal = {Advances in Mathematics},
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	Title = {Quantum and affine {Schubert} calculus and {Macdonald} polynomials},
	Volume = {312},
	Year = {2017}}

@article{KirillovNoumi,
	Author = {Kirillov, Anatol N. and Noumi, Masatoshi},
	Fjournal = {Duke Mathematical Journal},
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	Title = {Affine {Hecke} algebras and raising operators for {Macdonald} polynomials},
	Volume = {93},
	Year = {1998}}

@article{EtingofKirillov,
	Author = {Pavel I. Etingof and Alexander A. Kirillov},
	Fjournal = {Mathematical Research Letters},
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	Title = {Macdonald's polynomials and representations of quantum groups},
	Volume = {1},
	Year = {1994}}

@article{Cherednik,
	Author = {Cherednik, Ivan},
	Fjournal = {Annals of Mathematics},
	Journal = {Ann. of Math.},
	Number = {1},
	Pages = {191--216},
	Title = {Double affine {Hecke} algebras and {Macdonald}'s conjectures},
	Volume = {141},
	Year = {1995}}

@article{GorskyNegut,
	Author = {Gorsky, Eugene and Negu\c{t}, Andrei},
	Fjournal = {Journal de Math\'ematiques Pures et Appliqu\'ees. Neuvi\`eme S\'erie},
	Journal = {J. Math. Pures Appl. (9)},
	Number = {3},
	Pages = {403--435},
	Title = {Refined knot invariants and {Hilbert} schemes},
	Volume = {104},
	Year = {2015}}

@article{CarlssonMellit,
	Author = {Carlsson, Erik and Mellit, Anton},
	Date-Modified = {2019-05-04 15:35:11 +1000},
	Doi = {10.1090/jams/893 },
	Fjournal = {Journal of the American Mathematical Society},
	Journal = {J. Amer. Math. Soc.},
	Number = {3},
	Pages = {661--697},
	Title = {A proof of the shuffle conjecture},
	Volume = {31},
	Year = {2018}}

@article{BergeronPrevilleRatelle,
	Author = {Bergeron, Fran\c{c}ois and Pr\'eville-Ratelle, Louis-Fran\c{c}ois},
	Date-Modified = {2019-05-04 15:29:17 +1000},
	Doi = {10.4310/joc.2012.v3.n3.a4},
	Journal = {J. Combin.},
	Number = {3},
	Pages = {317--341},
	Title = {Higher trivariate diagonal harmonics via generalized {Tamari} posets},
	Volume = {3},
	Year = {2012},
	Bdsk-Url-1 = {https://doi.org/10.4310/joc.2012.v3.n3.a4}}

@book{Haglund-qt-catalan,
	Author = {Haglund, James},
	Publisher = {American Mathematical Society, Providence, RI},
	Series = {University {Lecture} {Series}},
	Title = {The $q$,$t$-{Catalan} numbers and the space of diagonal harmonics},
	Volume = {41},
	Year = {2008}}

@article{AndrewsKrattenthalerOrsinaPapi,
	Author = {Andrews, George E. and Krattenthaler, Christian and Orsina, Luigi and Papi, Paolo},
	Fjournal = {Transactions of the American Mathematical Society},
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	Number = {10},
	Pages = {3835--3853},
	Title = {ad-nilpotent {$\mathfrak b$}-ideals in {${\rm sl}(n)$} having a fixed class of nilpotence: combinatorics and enumeration},
	Volume = {354},
	Year = {2002}}

@article{HaglundHaimanLoehrRemmelUlyanov,
	Author = {Haglund, James and Haiman, Mark and Loehr, Nicholas A. and Remmel, Jeffrey B. and Ulyanov, Alexander},
	Date-Modified = {2019-05-04 15:40:39 +1000},
	Doi = {10.1215/s0012-7094-04-12621-1 },
	Fjournal = {Duke Mathematical Journal},
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	Title = {A combinatorial formula for the character of the diagonal coinvariants},
	Volume = {126},
	Year = {2005}}

@article{Haiman-vanishingTheorems,
	Author = {Haiman, Mark},
	Date-Modified = {2019-05-04 15:42:37 +1000},
	Doi = {10.1007/s002220200219 },
	Fjournal = {Inventiones mathematicae},
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	Number = {2},
	Pages = {371--407},
	Title = {Vanishing theorems and character formulas for the {Hilbert} scheme of points in the plane},
	Volume = {149},
	Year = {2002}}

@article{Haiman-hilbertSchemes,
	Author = {Haiman, Mark},
	Fjournal = {Journal of the American Mathematical Society},
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	Volume = {14},
	Year = {2001}}

@article{GarsiaHaiman-remarkableCatalanSequence,
	Author = {Garsia, Adriano M. and Haiman, Mark},
	Date-Modified = {2019-05-04 15:39:39 +1000},
	Doi = {10.1007/bf00243787 },
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	Title = {A remarkable $q,t$-{Catalan} sequence and $q$-{Lagrange} inversion},
	Volume = {5},
	Year = {1996}}

@article{GarsiaHaiman-BigradedModules,
	Author = {Garsia, Adriano M. and Haiman, Mark},
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	Year = {1996}}

@article{Haiman-conjectures,
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@article{GarsiaHaiman-gradedRepresentationModel,
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	Volume = {90},
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@unpublished{KallipolitiSulzgruber,
	Author = {Kallipoliti, Myrto and Sulzgruber, Robin},
	Note = {Personal communication (in preparation)},
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	Year = {2018}}

@unpublished{Bergeron-ePositivityConjecture,
	Author = {Bergeron, Fran\c{c}ois},
	Note = {Personal communication},
	Title = {The $e$-positivity conjecture for multivariate diagonal harmonics},
	Year = {2011}}

@unpublished{Thiery,
	Author = {Thi\'ery, Nicolas},
	Note = {\url{https://github.com/nthiery/harmonic-modules/}},
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	Year = {2018}}

@incollection{Haiman,
	Author = {Haiman, Mark},
	Booktitle = {Current developments in mathematics, 2002},
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	Publisher = {Int. Press, Somerville, MA},
	Title = {Combinatorics, symmetric functions, and {Hilbert} schemes},
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@article{Bergeron-multivariateDiagonalCoinvariantSpaces,
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	Date-Modified = {2019-05-04 15:28:22 +1000},
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@article{Chapoton-intervalsTamari,
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@article{FangPrevilleRatelle,
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@unpublished{CeballosPadrolSarmiento-geometryNuTamari,
	Author = {Ceballos, Cesar and Padrol, Arnau and Sarmiento, Camilo},
	Note = {To appear in Transactions of the American Mathematical Society. Preprint, \href{https://arxiv.org/abs/1608.04800}{\texttt{arXiv:1608.04800}}},
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@article{BousquetMelouChapuyPrevilleRatelle,
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@article{BousquetMelouFusyPrevilleRatelle,
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@misc{CeballosPadrolSarmiento-nuTamariSubwordComplexes,
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	Date-Modified = {2019-05-04 15:38:54 +1000},
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@article{SerranoStump,
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@unpublished{CeballosGonzalezDLeon,
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@article{MalvenutoReutenauer,
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@article{HivertNovelliThibon-algebraBinarySearchTrees,
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	Fjournal = {Theoretical Computer Science},
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	Number = {1},
	Pages = {129--165},
	Title = {The algebra of binary search trees},
	Volume = {339},
	Year = {2005}}

@inproceedings{Vargas,
	Author = {Yannic Vargas},
	Booktitle = {Proceedings of FPSAC'14},
	Date-Modified = {2019-05-04 16:04:47 +1000},
	Pages = {839--850},
	Publisher = {Discrete Math. Theor. Comput. Sci.},
	Title = {Hopf algebra of permutation pattern functions},
	Url = {https://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAT0172.1.html},
	Year = {2014}}

@article{Pilaud-brickAlgebra,
	Author = {Vincent Pilaud},
	Fjournal = {Journal of Combinatorial Theory. Series A},
	Journal = {J. Combin. Theory Ser. A},
	Pages = {418--457},
	Title = {Brick polytopes, lattice quotients, and {H}opf algebras},
	Volume = {155},
	Year = {2018}}

@misc{BergeronCeballosPilaud,
	Author = {Nantel Bergeron and Cesar Ceballos and Vincent Pilaud},
	Date-Modified = {2019-05-04 15:33:21 +1000},
	Eprint = {1807.03044},
	Eprinttype = {arxiv},
	Title = {Hopf dreams},
	Year = {2018}}

@article{Rubey,
	Author = {Rubey, Martin},
	Journal = {Advances in Applied Mathematics},
	Number = {2},
	Pages = {290--305},
	Title = {Maximal 0--1-fillings of moon polyominoes with restricted chain lengths and {RC}-graphs},
	Volume = {48},
	Year = {2012}}

@article{BergeronBilley,
	Author = {Nantel Bergeron and Sara Billey},
	Date-Modified = {2019-05-04 15:30:59 +1000},
	Doi = {10.1080/10586458.1993.10504567},
	Fjournal = {Experimental Mathematics},
	Journal = {Experimental Math.},
	Number = {4},
	Pages = {257--269},
	Title = {{RC}-graphs and {S}chubert polynomials},
	Volume = {2},
	Year = {1993},
	Bdsk-Url-1 = {https://doi.org/10.1080/10586458.1993.10504567}}

@incollection{PilaudStump-ELlabelings,
	Author = {Vincent Pilaud and Christian Stump},
	Booktitle = {Discrete Geometry and Optimization},
	Editor = {Karoly~Bezdek and Antoine~Deza and Yinyu~Ye},
	Pages = {213--248},
	Publisher = {Springer},
	Series = {Fields Institute Communications Series},
	Title = {EL-labelings and canonical spanning trees for subword complexes},
	Volume = {69},
	Year = {2013}}

@article{PilaudPocchiola,
	Author = {Vincent Pilaud and Michel Pocchiola},
	Date-Modified = {2019-05-04 15:47:51 +1000},
	Doi = {10.1007/s00454-012-9408-6 },
	Fjournal = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	Journal = {Discrete Comput. Geom.},
	Number = {1},
	Pages = {142--191},
	Title = {Multitriangulations, pseudotriangulations and primitive sorting networks},
	Volume = {48},
	Year = {2012}}

@article{PilaudSantos-multitriangulations,
	Author = {Vincent Pilaud and Francisco Santos},
	Fjournal = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science},
	Journal = {Discrete Comput. Geom.},
	Number = {2},
	Pages = {284--317},
	Title = {Multitriangulations as complexes of star polygons},
	Volume = {41},
	Year = {2009}}

@article{Stump,
	Author = {Christian Stump},
	Fjournal = {Journal of Combinatorial Theory. Series A},
	Journal = {J. Combin. Theory Ser. A},
	Number = {6},
	Pages = {1794--1800},
	Title = {A new perspective on $k$-triangulations},
	Volume = {118},
	Year = {2011}}

@misc{Woo,
	Author = {Woo, Alexander},
	Date-Modified = {2019-05-04 16:07:08 +1000},
	Eprint = {math/0407160},
	Eprinttype = {arxiv},
	Title = {Catalan numbers and Schubert polynomials for $w = 1 (n+1) \dots 2$},
	Year = {2004}}

@phdthesis{Pilaud-these,
	Author = {Vincent Pilaud},
	Note = {Available online \href{http://arxiv.org/abs/1009.1605}{\texttt{arXiv:1009.1605}}},
	School = {Universit\'e Paris 7 \& Universidad de Cantabria},
	Title = {Multitriangulations, pseudotriangulations and some problems of realization of polytopes},
	Year = {2010}}

@article{KnutsonMiller-GroebnerGeometry,
	Author = {Knutson, Allen and Miller, Ezra},
	Date-Modified = {2019-05-04 15:45:02 +1000},
	Doi = {10.4007/annals.2005.161.1245 },
	Fjournal = {Annals of Mathematics. Second Series},
	Journal = {Ann. of Math. (2)},
	Number = {3},
	Pages = {1245--1318},
	Title = {Gr\"obner geometry of {S}chubert polynomials},
	Volume = {161},
	Year = {2005}}

@article{KnutsonMiller-subwordComplex,
	Author = {Allen Knutson and Ezra Miller},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Number = {1},
	Pages = {161--176},
	Title = {Subword complexes in {C}oxeter groups},
	Volume = {184},
	Year = {2004}}

@article{PilaudStump-brickPolytopes,
	Author = {Vincent Pilaud and Christian Stump},
	Fjournal = {Advances in Mathematics},
	Journal = {Adv. Math.},
	Pages = {1--61},
	Title = {Brick polytopes of spherical subword complexes and generalized associahedra},
	Volume = {276},
	Year = {2015}}

@article{PilaudSantos-brickPolytope,
	Author = {Vincent Pilaud and Francisco Santos},
	Fjournal = {European Journal of Combinatorics},
	Journal = {European~J.~Combin.},
	Number = {4},
	Pages = {632--662},
	Title = {The brick polytope of a sorting network},
	Volume = {33},
	Year = {2012}}

@unpublished{OEIS,
	Key = {{OEIS}},
	Note = {Published electronically at \url{http://oeis.org}},
	Title = {The {O}n-{L}ine {E}ncyclopedia of {I}nteger {S}equences},
	Year = {2010}}

@manual{Sage,
	Author = {The {S}age developers},
	Note = {\url{http://www.sagemath.org}},
	Title = {{S}age {M}athematics {S}oftware},
	Year = {2016}}

@manual{SageCombinat,
	Author = {The {S}age-{C}ombinat community},
	Note = {\url{http://wiki.sagemath.org/combinat}},
	Title = {{S}age-{C}ombinat: enhancing {S}age as a toolbox for computer exploration in algebraic combinatorics},
	Year = {2016}}