% This is an example bibliography file for FPSAC submissions.

@article{greenwade93,
  author        = {George D. Greenwade},
  date-modified = {2016-08-11 21:04:25 +0000},
  journal       = {TUGBoat},
  number        = {3},
  pages         = {342--351},
  title         = {The {C}omprehensive {T}ex {A}rchive {N}etwork ({CTAN})},
  url           = {https://www.google.com},
  volume        = {14},
  year          = {1993},
  bdsk-url-1    = {https://www.google.com}
}

@article{MR4,
  author     = {Corliss, J. J.},
  title      = {Upper limits to the real roots of a real algebraic equation},
  journal    = {Amer. Math. Monthly},
  fjournal   = {The American Mathematical Monthly},
  volume     = {46},
  year       = {1939},
  pages      = {334--338},
  issn       = {0002-9890},
  mrclass    = {09.0X},
  mrnumber   = {0000004},
  mrreviewer = {O. Sz\'asz},
  doi        = {10.2307/2302887}
}


@article {bib:EhrenborgHapp,
    AUTHOR = {Ehrenborg, Richard and Happ, Alex},
     TITLE = {Parking cars of different sizes},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {American Mathematical Monthly},
    VOLUME = {123},
      YEAR = {2016},
    NUMBER = {10},
     PAGES = {1045--1048},
   MRCLASS = {05A15 (05A19)},
  MRNUMBER = {3593646},
MRREVIEWER = {Joseph Kung},
       DOI = {10.4169/amer.math.monthly.123.10.1045},
       URL = {https://doi-org.ezproxy2.williams.edu/10.4169/amer.math.monthly.123.10.1045},
}

@article {bib:SamSpiro,
    AUTHOR = {Spiro, Sam},
     TITLE = {Subset parking functions},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {22},
      YEAR = {2019},
    NUMBER = {7},
     PAGES = {Art. 19.7.3, 15},
   MRCLASS = {05A15 (05A19)},
  MRNUMBER = {4040978},
MRREVIEWER = {Roberto Tauraso},
}

@misc{bib:stanleydocpollakproof,
    title={Parking Functions},
    author={R. P. Stanley},
    year={2018, retrieved October 8, 2020},
    URL={http://www-math.mit.edu/~rstan/transparencies/parking.pdf}
}

@article{bib:kNaplesStatistics,
    title={Counting k-{N}aples parking functions through permutations and the k-{N}aples area statistic},
    author={L. Colmenarejo and P. E. Harris and Z. Jones and C. Keller and A. Ramos R. and Eunice S. and A. R. Vindas-Meléndez},
    year={2020},
    eprint={2009.01124v1},
    archivePrefix={},
    journal={ArXiv},
    primaryClass={math.CO},
    note={\url{https://arxiv.org/pdf/2009.01124.pdf}}
}


@article{bib:ButlerPFonTrees,
    author = {S. Butler and R. Graham and C. Yan},
    year = {2017},
    pages = {168-185},
    title = {Parking distributions on trees
    },
    volume = {65},
    journal = {European Journal of Combinatorics},
    doi = {https://doi.org/10.1016/j.ejc.2017.06.003},
}


@article{bib:NaplesPF,
    author = {A. Christensen and P. E. Harris and Z. Jones and M. Loving and A. Ramos Rodr\'{i}guez and J. Rennie and G. Rojas Kirby},
    year = {2020},
    pages = {\#P1.33},
    title = {A generalization of parking functions allowing backward movement
    },
    volume = {27(1)},
    journal = {The Electronic Journal of Combinatorics},
    doi = {https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p33/8024},
}


@article{bib:mparkingfunctions,
    author={J.C. Novelli and J.Y. Thibon},
    year={2020},
    title={Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions},
    eprint={1403.5962v3},
    archivePrefix={},
    journal={ArXiv},
    primaryClass={math.CO},
    note = {\url{https://arxiv.org/pdf/1403.5962v3.pdf}}
}

@article{bib:Colaric2020IntervalPF,
    AUTHOR = {Colaric, Emma and DeMuse, Ryan and Martin, Jeremy L. and Yin, Mei},
     TITLE = {Interval parking functions},
   JOURNAL = {Adv. in Appl. Math.},
  FJOURNAL = {Advances in Applied Mathematics},
    VOLUME = {123},
      YEAR = {2021},
     PAGES = {Paper No. 102129, 17},
   MRCLASS = {05E16 (05A05 06D99 20F55)},
  MRNUMBER = {4175420},
MRREVIEWER = {Christian\ Stump},
       DOI = {10.1016/j.aam.2020.102129},
       URL = {https://doi.org/10.1016/j.aam.2020.102129},
      note = {\href{https://arxiv.org/pdf/2006.09321.pdf}{arXiv:2006.09321}}
}

@article{bib:CountingDefectivePF,
    author={P. J. Cameron and D. Johannsen and T. Prellberg and P. Schweitzer},
    year={2008},
    title={Counting Defective Parking Functions},
    eprint={0803.0302v2},
    journal={ArXiv},
    primaryClass={math.CO},
    note={\url{https://arxiv.org/pdf/0803.0302v2.pdf}}
}

@misc{bib:recursionproof,
  author={N. Shales},
  title={Recursively counting a parking function},
  year={retrieved October 10, 2020},
  note = {\url{https://math.stackexchange.com/questions/2718303/recursively-counting-a-parking-function}},
}

@article{bib:ParkingCompletions,
    AUTHOR = {Adeniran, Ayomikun and Butler, Steve and Dorpalen-Barry, Galen and Harris, Pamela E. and Hettle, Cyrus and Liang, Qingzhong and Martin, Jeremy L. and Nam, Hayan},
     TITLE = {Enumerating parking completions using {J}oin and {S}plit},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {27},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {Paper No. 2.44, 19},
   MRCLASS = {05A15 (05A19)},
  MRNUMBER = {4245099},
MRREVIEWER = {David\ Callan},
       DOI = {10.37236/9194},
       URL = {https://doi.org/10.37236/9194},
}




@article{Konheim1966,
    author = {A. Konheim and B. Weiss},
    title = {An Occupancy Discipline and Applications},
    JOURNAL = {SIAM J. Appl. Math.},
    FJOURNAL = {SIAM Journal on Applied Mathematics},
    volume = {14},
    number = {6},
    pages = {1266-1274},
    year = {1966},
    doi = {10.1137/0114101},
}

@unpublished{bib:PFCYOA,
    author={J. Carlson and A. Christensen and P. E. Harris and Z. Jones and A. Ramos Rodr\'{i}guez},
    title={Parking {F}unctions: {C}hoose {Y}our {O}wn {A}dventure},
    year={2020},
    note={\href{https://arxiv.org/pdf/2001.04817.pdf}{arXiv:2001.04817}},
}

@misc{bib:GirlsAnglePart1,
    title={Honk! {H}onk!, {P}art 1: {A}n {I}ntroduction to {P}arking {F}unctions},
    author={K. P. Hadaway and P. E. Harris},
    year={2021},
    note={\url{http://www.girlsangle.org/page/bulletin-archive/GABv14n02E.pdf#page=15}}
}

@misc{bib:GirlsAnglePart2,
    title={Honk! {H}onk!, {P}art 2: {A}n {I}ntroduction to {P}arking {F}unctions},
    author={K. P. Hadaway and P. E. Harris},
    year={2021},
    note={\url{http://www.girlsangle.org/page/bulletin-archive/GABv14n03E.pdf#page=14}}
}

@misc{bib:HadawayUndergradThesis,
    title={On {C}ombinatorial {P}roblems of {G}eneralized {P}arking {F}unctions},
    author={K. P. Hadaway},
    year={2021},
    note={Williams College Honors Thesis}
}

@unpublished{bib:Inversions+MajorIndex,
    author={M. Notick},
    year={2009},
    title={A Bijective Proof of a Major Index Theorem of Garsia and Gessel},
    note={\href{https://arxiv.org/pdf/0906.0377.pdf}{arXiv:0906.0377}}
}

@article{bib:DescentsInPF,
    AUTHOR = {Schumacher, Paul R. F.},
     TITLE = {Descents in parking functions},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {21},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {Art. 18.2.3, 8 pp.},
    doi = {https://doi.org/10.37236/9194},
    URL = {https://www.emis.de/journals/JIS/VOL21/Schumacher/schu5.pdf},
}

 
@article{bib:Cayley,
    author = {Cayley, A.},
    year = {1859},
    pages = {374-378},
    title = {On the analytical forms called trees, second part},
    volume = {18 (121)},
    journal = {Philosophical Magazine},
    doi = {doi:10.1017/CBO9780511703706.026},
}




@article{reiner2004cyclic,
  title={The cyclic sieving phenomenon},
  author={Reiner, Victor and Stanton, Dennis and White, Dennis},
  journal={Journal of Combinatorial Theory, Series A},
  volume={108},
  number={1},
  pages={17--50},
  year={2004},
  publisher={Elsevier}
}

@unpublished{adams2024cyclic,
      title={Cyclic sieving on permutations -- an analysis of maps and statistics in the FindStat database}, 
      author={Ashleigh Adams and Jennifer Elder and Nadia Lafreni\`{e}re and Erin McNicholas and Jessica Striker and Amanda Welch},
      year={2024},
    note={\href{https://arxiv.org/abs/2402.16251}{arXiv:2402.16251}}
}

@misc{unit_perm,
   author = {Chaves Meyles, Lucas and
            Harris, Pamela E. 
            and Jordaan, Richter 
            and Rojas Kirby, Gordon  
            and  Sehayek, Sam 
            and Spingarn, Ethan },
   title = {Unit-interval Parking Functions and the Permutohedron},
   year = {2023},
eprint = {2305.15554},
eprinttype = {arXiv},
   }

@article{elder2023homomesies,
      title={Homomesies on permutations -- an analysis of maps and statistics in the FindStat database}, 
      author={Jennifer Elder and Nadia Lafreni\`{e}re and Erin McNicholas and Jessica Striker and Amanda Welch},
      year={2024},
      journal={Math. Comp.},
    volume={93},
issue={346},
pages = {921-976},
note={\emph{ArXiv version}, \url{https://arxiv.org/abs/2206.13409}}
}

@misc{dowling2023homomesy,
      title={Homomesy on permutations with toggling actions}, 
      author={William Dowling and Nadia Lafreniere},
      year={\emph{ArXiv}, 2023},
      eprint={2312.02383},
      archivePrefix={arXiv},
      primaryClass={math.CO},
    note={\url{https://arxiv.org/abs/2312.02383}}
}

@misc{joseph2018whirling,
      title={Whirling injections, surjections, and other functions between finite sets}, 
      author={Michael Joseph and James Propp and Tom Roby},
      year={2018},
      eprint={1711.02411},
      archivePrefix={arXiv},
      primaryClass={math.CO},
    note={\url{https://arxiv.org/abs/1711.02411}}
}

@article {bradt2024unit,
    AUTHOR = {Bradt, S. Alex and Elder, Jennifer and Harris, Pamela E. and Kirby, Gordon Rojas and Reutercrona, Eva and Wang, Yuxuan and Whidden, Juliet},
     TITLE = {Unit interval parking functions and the r-{F}ubini numbers},
   JOURNAL = {Matematica},
  FJOURNAL = {La Matematica},
    VOLUME = {3},
      YEAR = {2024},
    NUMBER = {1},
     PAGES = {370--384},
   MRCLASS = {05A15},
  MRNUMBER = {4723221},
       DOI = {10.1007/s44007-024-00089-y},
       URL = {https://doi.org/10.1007/s44007-024-00089-y},
}
    

@book {stanley2012enumerative,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}olume 1},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {49},
   EDITION = {Second},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2012},
     PAGES = {xiv+626},
}

@article {foata,
    AUTHOR = {Foata, Dominique},
     TITLE = {On the {N}etto inversion number of a sequence},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {19},
      YEAR = {1968},
     PAGES = {236--240},
   MRCLASS = {05.10},
  MRNUMBER = {223256},
MRREVIEWER = {P.\ Erd\H os},
       DOI = {10.2307/2036179},
       URL = {https://doi.org/10.2307/2036179},
}

@article {MacMahon,
    AUTHOR = {MacMahon, P. A.},
     TITLE = {Two {A}pplications of {G}eneral {T}heorems in {C}ombinatory
              {A}nalysis},
   JOURNAL = {Proc. London Math. Soc. (2)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Second Series},
    VOLUME = {15},
      YEAR = {1916},
     PAGES = {314--321},
   MRCLASS = {99-04},
  MRNUMBER = {1576566},
       DOI = {10.1112/plms/s2-15.1.314},
       URL = {https://doi.org/10.1112/plms/s2-15.1.314},
}

@article {PR2015,
    AUTHOR = {Propp, James and Roby, Tom},
     TITLE = {Homomesy in products of two chains},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {22},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {Paper 3.4, 29 pages},
   MRCLASS = {05E18 (06A07 06A11)},
  MRNUMBER = {3367853},
       DOI = {10.37236/3579},
}

@article{berget_constructions_2011,
    AUTHOR = {Berget, Andrew and Eu, Sen-Peng and Reiner, Victor},
     TITLE = {Constructions for cyclic sieving phenomena},
   JOURNAL = {SIAM J. Discrete Math.},
  FJOURNAL = {SIAM Journal on Discrete Mathematics},
    VOLUME = {25},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {1297--1314},
       DOI = {10.1137/100803596},
       URL = {https://doi.org/10.1137/100803596},
}


@article{elder2024parking,
    AUTHOR = {Elder, Jennifer and Harris, Pamela E. and Kretschmann, Jan and
              Mart\'inez Mori, J. Carlos},
     TITLE = {Parking functions, {F}ubini rankings, and {B}oolean intervals
              in the weak order of {$\mathfrak{S}_n$}},
   JOURNAL = {J. Comb.},
  FJOURNAL = {Journal of Combinatorics},
    VOLUME = {16},
      YEAR = {2025},
    NUMBER = {1},
     PAGES = {65--89},
       DOI = {10.4310/joc.241216213152},
       URL = {https://doi.org/10.4310/joc.241216213152},
}

@misc{baril2018descent,
      title={Descent distribution on Catalan words avoiding a pattern of length at most three}, 
      author={Jean-Luc Baril and Sergey Kirgizov and Vincent Vajnovszki},
      year={2018},
      eprint={1803.06706},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@unpublished{aguilarfraga2024interval,
      title={Interval and $\ell$-interval Rational Parking Functions}, 
      author={Tom\'{a}s Aguilar-Fraga and Jennifer Elder and Rebecca E. Garcia and Kimberly P. Hadaway and Pamela E. Harris and Kimberly J. Harry and Imhotep B. Hogan and Jakeyl Johnson and Jan Kretschmann and Kobe Lawson-Chavanu and J. Carlos Mart\'{i}nez Mori and Casandra D. Monroe and Daniel Quiñonez and Dirk Tolson III and Dwight Anderson Williams II},
      year={2024},
      note={\href{https://arxiv.org/pdf/2311.14055.pdf}{arXiv:2311.14055}}
}


@manual{sage,
 author = {William\thinspace{}A. Stein and others},
 key    = {Sage Math},
 URL   = {http://www.sagemath.org},
 organization  = {The Sage Development Team},
 title  = {{S}age {M}athematics {S}oftware ({V}ersion 9.4)},
 year   = {2022},
}

@manual{SMC,
  Key          = {CoCalc},
  Author       = {{SageMath Inc.}},
  Title        = {CoCalc Collaborative Computation Online},
  note         = {{\tt https://cocalc.com/}},
  Year         = {2022},
}

@article {bib:ColmenarejoHarris,
    AUTHOR = {Colmenarejo, Laura and Harris, Pamela E. and Jones, Zakiya and Keller, Christo and Ramos Rodr\'iguez, Andr\'es and Sukarto, Eunice and Vindas-Mel\'endez, Andr\'es R.},
     TITLE = {Counting {$k$}-{N}aples parking functions through permutations and the {$k$}-{N}aples area statistic},
   JOURNAL = {Enumer. Comb. Appl.},
  FJOURNAL = {Enumerative Combinatorics and Applications},
    VOLUME = {1},
      YEAR = {2021},
    NUMBER = {2},
     PAGES = {Paper No. S2R11, 16},
  MRNUMBER = {4398562},
       DOI = {10.54550/eca2021v1s2r11},
       URL = {https://doi.org/10.54550/eca2021v1s2r11},
}

@article{stanley1976binomial,
  title={Binomial posets, M{\"o}bius inversion, and permutation enumeration},
  author={Stanley, Richard P},
  journal={Journal of Combinatorial Theory, Series A},
  volume={20},
  number={3},
  pages={336--356},
  year={1976},
  publisher={Elsevier},
  DOI = {10.1016/0097-3165(76)90028-5},
  URL = {https://doi.org/10.1016/0097-3165(76)90028-5},
}

@article{shareshian_eulerian_2010,
	title = {Eulerian quasisymmetric functions},
	volume = {225},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0001870810001933},
	doi = {10.1016/j.aim.2010.05.009},
	abstract = {We introduce a family of quasisymmetric functions called Eulerian quasisymmetric functions, which specialize to enumerators for the joint distribution of the permutation statistics, major index and excedance number on permutations of fixed cycle type. This family is analogous to a family of quasisymmetric functions that Gessel and Reutenauer used to study the joint distribution of major index and descent number on permutations of fixed cycle type. Our central result is a formula for the generating function for the Eulerian quasisymmetric functions, which specializes to a new and surprising q-analog of a classical formula of Euler for the exponential generating function of the Eulerian polynomials. This q-analog computes the joint distribution of excedance number and major index, the only of the four important Euler-Mahonian distributions that had not yet been computed. Our study of the Eulerian quasisymmetric functions also yields results that include the descent statistic and refine results of Gessel and Reutenauer. We also obtain q-analogs, (q, p)-analogs and quasisymmetric function analogs of classical results on the symmetry and unimodality of the Eulerian polynomials. Our Eulerian quasisymmetric functions refine symmetric functions that have occurred in various representation theoretic and enumerative contexts including MacMahon’s study of multiset derangements, work of Procesi and Stanley on toric varieties of Coxeter complexes, Stanley’s work on chromatic symmetric functions, and the work of the authors on the homology of a certain poset introduced by Bj¨orner and Welker.},
	language = {en},
	number = {6},
	urldate = {2023-12-29},
	journal = {Advances in Mathematics},
	author = {Shareshian, John and Wachs, Michelle L.},
	month = dec,
	year = {2010},
	pages = {2921--2966},
	file = {Shareshian and Wachs - 2010 - Eulerian quasisymmetric functions.pdf:/Users/kylecelano/Zotero/storage/GED2X2IK/Shareshian and Wachs - 2010 - Eulerian quasisymmetric functions.pdf:application/pdf},
}

@article{Marberg_2021,
   title={Linear Compactness and Combinatorial Bialgebras},
   volume={28},
   ISSN={1077-8926},
   url={http://dx.doi.org/10.37236/9459},
   DOI={10.37236/9459},
   number={3},
   journal={Electron. J. Combin.},
   author={Marberg, Eric},
   year={2021},
   month=jul }



@article{haiman_conjectures_1994,
	title = {Conjectures on the {Quotient} {Ring} by {Diagonal} {Invariants}},
	volume = {3},
	url = {https://doi.org/10.1023/A:1022450120589},
	doi = {10.1023/A:1022450120589},
	abstract = {We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring \$\${\textbackslash}mathbb\{Q\}[x\_1 , {\textbackslash}ldots ,x\_n ,y\_1 , {\textbackslash}ldots ,y\_n ]\$\$in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = \{x1, ..., xn\} is classical. Introducing the second set of variables leads to a ring about which little is yet understood, but for which there is strong evidence of deep connections with many fundamental results of enumerative combinatorics, as well as with algebraic geometry and Lie theory.},
	language = {en},
	number = {1},
	urldate = {2024-06-28},
	journal = {Journal of Algebraic Combinatorics},
	author = {Haiman, Mark D.},
	month = jan,
	year = {1994},
	keywords = {Coxeter group, diagonal harmonics, invariant},
	pages = {17--76},
	file = {Full Text PDF:/Users/kylecelano/Zotero/storage/JURV3JAS/Haiman - 1994 - Conjectures on the Quotient Ring by Diagonal Invar.pdf:application/pdf},
}


@misc{armstrong2014rationalparkingfunctionscatalan,
      title={Rational parking functions and Catalan numbers}, 
      author={Drew Armstrong and Nicholas A. Loehr and Gregory S. Warrington},
      year={2014},
      eprint={1403.1845},
      archivePrefix={arXiv},
      primaryClass={math.CO},
      url={https://arxiv.org/abs/1403.1845}, 
}


@misc{shareshian_chromatic_2016,
	title = {Chromatic quasisymmetric functions},
	url = {http://arxiv.org/abs/1405.4629},
	abstract = {We introduce a quasisymmetric refinement of Stanley's chromatic symmetric function. We derive refinements of both Gasharov's Schur-basis expansion of the chromatic symmetric function and Chow's expansion in Gessel's basis of fundamental quasisymmetric functions. We present a conjectural refinement of Stanley's power sum basis expansion, which we prove in special cases. We describe connections between the chromatic quasisymmetric function and both the \$q\$-Eulerian polynomials introduced in our earlier work and, conjecturally, representations of symmetric groups on cohomology of regular semisimple Hessenberg varieties, which have been studied by Tymoczko and others. We discuss an approach, using the results and conjectures herein, to the \$e\$-positivity conjecture of Stanley and Stembridge for incomparability graphs of \$(3+1)\$-free posets.},
	urldate = {2023-03-31},
	author = {Shareshian, John and Wachs, Michelle L.},
	month = mar,
	year = {2016},
	note = {arXiv:1405.4629 [math]},
	file = {Shareshian and Wachs - 2016 - Chromatic quasisymmetric functions.pdf:/Users/kylecelano/Zotero/storage/PNBGLTFD/Shareshian and Wachs - 2016 - Chromatic quasisymmetric functions.pdf:application/pdf},
}

@article{carlsson2018proof,
  title={A proof of the shuffle conjecture},
  author={Carlsson, Erik and Mellit, Anton},
  journal={Journal of the American Mathematical Society},
  volume={31},
  number={3},
  pages={661--697},
  year={2018}
}

@article{NOVELLI2021105305,
title = {Noncommutative unicellular LLT polynomials},
journal = {Journal of Combinatorial Theory, Series A},
volume = {177},
pages = {105305},
year = {2021},
doi = {https://doi.org/10.1016/j.jcta.2020.105305},
url = {https://www.sciencedirect.com/science/article/pii/S0097316520300972},
author = {Jean-Christophe Novelli and Jean-Yves Thibon},
keywords = {Noncommutative symmetric functions, Quasi-symmetric functions, LLT polynomials},
abstract = {It is known that unicellular LLT polynomials are related to the quasi-symmetric chromatic polynomials of certain graphs by the (t−1)-transform of symmetric functions. We investigate the extension of this transformation to various combinatorial Hopf algebras and prove a noncommutative version of this property.}
} 




@unpublished{cerbai2024caylerianpolynomials,
      title={{C}aylerian polynomials}, 
      author={Giulio Cerbai and Anders Claesson},
      year={2024},
      note={\href{https://arxiv.org/abs/2310.01270}{arXiv:2310.01270}}, 
}

@article{caylerian,
    AUTHOR = {Cerbai, Giulio and Claesson, Anders},
     TITLE = {Caylerian polynomials},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {347},
      YEAR = {2024},
    NUMBER = {12},
     PAGES = {Paper No. 114177, 22 pp.},
       DOI = {10.1016/j.disc.2024.114177},
       URL = {https://doi.org/10.1016/j.disc.2024.114177},
}

@unpublished{pan2017pairedpatternslatticepaths,
      title={Paired patterns in lattice paths}, 
      author={Ran Pan and Jeffrey B. Remmel},
      year={2017},
      note={\href{https://arxiv.org/abs/1601.07988}{arXiv:1601.07988}},
}




@article{avalos_sequences_2020,
	title = {Sequences, q-multinomial {Identities}, {Integer} {Partitions} with {Kinds}, and {Generalized} {Galois} {Numbers}},
	volume = {3},
	journal = {The PUMP Journal of Undergraduate Research},
	author = {Avalos, Adrian and Bly, Mark},
	month = jun,
	year = {2020},
	pages = {72--94},
        note = {Published online at \url{https://journals.calstate.edu/pump/article/view/2254}},
}


@article{Hanoi,
author = {Yasmin Aguillon and Dylan Alvarenga and Pamela E. Harris and Surya Kotapati and J. Carlos Martínez Mori and Casandra D. Monroe and Zia Saylor and Camelle Tieu and Dwight Anderson Williams II},
title = {On Parking Functions and The Tower of Hanoi},
journal = {The American Mathematical Monthly},
pages = {1-7},
year  = {2023},
publisher = {Taylor & Francis},
doi = {10.1080/00029890.2023.2206311}
}

@misc{cruz2024discretestatisticsparkingfunctions,
      title={On some discrete statistics of parking functions}, 
      author={Ari Cruz and Pamela E. Harris and Kimberly J. Harry and Jan Kretschmann and Matt McClinton and Alex Moon and John O. Museus and Eric Redmon},
      year={2024},
      eprint={2312.16786},
      archivePrefix={arXiv},
      primaryClass={math.CO},
      url={https://arxiv.org/abs/2312.16786}, 
}

@article{CZABARKA20182789,
title = {Enumerations of peaks and valleys on non-decreasing Dyck paths},
journal = {Discrete Mathematics},
volume = {341},
number = {10},
pages = {2789-2807},
year = {2018},
doi = {https://doi.org/10.1016/j.disc.2018.06.032},
url = {https://www.sciencedirect.com/science/article/pii/S0012365X18302036},
author = {Éva Czabarka and Rigoberto Flórez and Leandro Junes and José L. Ramírez},
keywords = {Non-decreasing Dyck path, Generating function, Valley, Peak, Fibonacci number},
abstract = {A valley in a Dyck path is a local minimum, and a peak is a local maximum. A Dyck path is non-decreasing if the y-coordinates of the valleys of the path valley form anon-decreasing sequence. In this paper we provide some statistics about peaks and valleys in non-decreasing Dyck paths, such as their total number, the number of low and high valleys, low and high peaks, etc. Our methods include bijective proofs, recursive relations, and the symbolic method for generating functions.}
}

@article{Foata1978,
author = {Foata, Dominique and Schützenberger, Marcel-Paul},
title = {Major Index and Inversion Number of Permutations},
journal = {Mathematische Nachrichten},
volume = {83},
number = {1},
pages = {143-159},
doi = {https://doi.org/10.1002/mana.19780830111},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.19780830111},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.19780830111},
year = {1978}
}

@article {Billey_Permu,
    AUTHOR = {Billey, Sara and Burdzy, Krzysztof and Sagan, Bruce E.},
    TITLE = {Permutations with given peak set},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {16},
      YEAR = {2013},
    NUMBER = {6},
     PAGES = {Article 13.6.1, 18},
   MRCLASS = {05A05 (05A10 05A15)},
  MRNUMBER = {3083179},
MRREVIEWER = {Svetlana Poznanovi\'{c}},
}

@article{SANYAL2018605,
title = {Lipschitz polytopes of posets and permutation statistics},
journal = {Journal of Combinatorial Theory, Series A},
volume = {158},
pages = {605-620},
year = {2018},
doi = {https://doi.org/10.1016/j.jcta.2018.04.006},
url = {https://www.sciencedirect.com/science/article/pii/S0097316518300591},
author = {Raman Sanyal and Christian Stump},
}

@article{GONZALEZ2023113439,
title = {Pinnacle sets of signed permutations},
journal = {Discrete Mathematics},
volume = {346},
number = {7},
pages = {113439},
year = {2023},
doi = {https://doi.org/10.1016/j.disc.2023.113439},
url = {https://www.sciencedirect.com/science/article/pii/S0012365X23001255},
author = {Nicolle González and Pamela E. Harris and Gordon {Rojas Kirby} and Mariana {Smit Vega Garcia} and Bridget Eileen Tenner},
keywords = {05A05, Pinnacle sets, Admissible pinnacle sets, Signed permutations},
abstract = {Pinnacle sets record the values of the local maxima for a given family of permutations. They were introduced by Davis-Nelson-Petersen-Tenner as a dual concept to that of peaks, previously defined by Billey-Burdzy-Sagan. In recent years pinnacles and admissible pinnacles sets for the type A symmetric group have been widely studied. In this article we define the pinnacle set of signed permutations of types B and D. We give a closed formula for the number of type B/D admissible pinnacle sets and answer several other related enumerative questions.}
}

@article{sum_stat,
    author ={Yukun Yao and Doron Zeilberger},
title={An Experimental Mathematics Approach to the Area Statistic of Parking Functions},
journal={Math Intelligencer}, 
volume={41}, 
pages={1–8},
year={2019}
}

@article{DEUTSCH1999167,
title = {Dyck path enumeration},
journal = {Discrete Mathematics},
volume = {204},
number = {1},
pages = {167-202},
year = {1999},
note = {Selected papers in honor of Henry W. Gould},
doi = {https://doi.org/10.1016/S0012-365X(98)00371-9},
url = {https://www.sciencedirect.com/science/article/pii/S0012365X98003719},
author = {Emeric Deutsch},
keywords = {Dyck paths, Combinatorial enumeration, Generating functions, Catalan numbers, Fine numbers, Narayana numbers, Ordered trees, Parallelogram polyominoes, Non-crossing partitions, Similarity relations},
abstract = {An elementary technique is used for the enumeration of Dyck paths according to various parameters. For several of the considered parameters the generating function is expressed in terms of the Narayana function. Many enumeration results are obtained, some of which involve the Fine numbers.}
}

@misc{fulman2021jointdistributiondescentssigns,
    AUTHOR = {Fulman, Jason and Kim, Gene B. and Lee, Sangchul and Petersen,
              T. Kyle},
     TITLE = {On the joint distribution of descents and signs of
              permutations},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {28},
      YEAR = {2021},
    NUMBER = {3},
     PAGES = {Paper No. 3.37, 30 pp.},
       DOI = {10.37236/10222},
       URL = {https://doi.org/10.37236/10222},
}

@article{desarmenien1992signed,
    AUTHOR = {D\'esarm\'enien, Jacques and Foata, Dominique},
     TITLE = {The signed {E}ulerian numbers},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {99},
      YEAR = {1992},
    NUMBER = {1-3},
     PAGES = {49--58},
       DOI = {10.1016/0012-365X(92)90364-L},
       URL = {https://doi.org/10.1016/0012-365X(92)90364-L},
}

@article{WACHS199259,
title = {An involution for signed Eulerian numbers},
journal = {Discrete Mathematics},
volume = {99},
number = {1},
pages = {59-62},
year = {1992},
doi = {https://doi.org/10.1016/0012-365X(92)90365-M},
url = {https://www.sciencedirect.com/science/article/pii/0012365X9290365M},
author = {Michelle L. Wachs},
abstract = {We give a bijective derivation of a result of Désarménien and Foata on the relationship between signed Eulerian numbers and the classical Eulerian numbers. The bijection is also used to obtain some additional results.}
}

@book{stanley1999enumerative,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {62},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1999},
     PAGES = {xii+581},
       DOI = {10.1017/CBO9780511609589},
       URL = {https://doi.org/10.1017/CBO9780511609589},
}



@article{Shin2008,
     author = {Shin, Heesung},
     title = {A New Bijection Between Forests and Parking Functions},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0810.0427}
}

@article{stanley1997parking,
  title={Parking functions and noncrossing partitions.},
  author={Stanley, Richard P},
  journal={The Electronic Journal of Combinatorics [electronic only]},
  volume={4},
  number={2},
  pages={v4i2r20--pdf},
  year={1997},
  publisher={Prof. Andr{\'e} K{\"u}ndgen, Deptartment of Mathematics, California State University~…}
}

@book{stanley2015catalan,
  title={Catalan numbers},
  author={Stanley, Richard P},
  year={2015},
  PAGES = {viii+215},
  publisher={Cambridge University Press, New York},
  DOI = {10.1017/CBO9781139871495},
  URL = {https://doi.org/10.1017/CBO9781139871495},
}

@article{kreweras1980famille,
     TITLE = {Une famille de polyn\^omes ayant plusieurs propri\'et\'es
              \'enumeratives},
   JOURNAL = {Period. Math. Hungar.},
  FJOURNAL = {Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai
              Mathematical Society},
    VOLUME = {11},
      YEAR = {1980},
    NUMBER = {4},
     PAGES = {309--320},
       DOI = {10.1007/BF02107572},
       URL = {https://doi.org/10.1007/BF02107572},
}


@article{francon_acyclic_1975,
	title = {Acyclic and parking functions},
	volume = {18},
  DOI = {10.1016/0097-3165(75)90063-1},
  URL = {https://doi.org/10.1016/0097-3165(75)90063-1},
	abstract = {A large class of one-to-one correspondences is given between acyclic and parking functions, generalizing a previous construction given by Foata and Riordan.},
   JOURNAL = {J. Combinatorial Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
	author = {Françon, Jean},
	year = {1975},
	pages = {27--35},
}



@article {MR2115257,
    AUTHOR = {Haglund, J. and Haiman, M. and Loehr, N. and Remmel, J. B. and
              Ulyanov, A.},
     TITLE = {A combinatorial formula for the character of the diagonal
              coinvariants},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {126},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {195--232},
   MRCLASS = {05E10 (05A30 20C30)},
  MRNUMBER = {2115257},
MRREVIEWER = {Edward\ E.\ Allen},
       DOI = {10.1215/S0012-7094-04-12621-1},
       URL = {https://doi.org/10.1215/S0012-7094-04-12621-1},
}


@article {RemmelWilsonTimothy,
    AUTHOR = {Remmel, Jeffrey B. and Wilson, Andrew Timothy},
     TITLE = {An extension of {M}ac{M}ahon's equidistribution theorem to
              ordered set partitions},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {134},
      YEAR = {2015},
     PAGES = {242--277},
   MRCLASS = {05A18 (05A15)},
  MRNUMBER = {3345306},
MRREVIEWER = {Damir\ Yeliussizov},
       DOI = {10.1016/j.jcta.2015.03.012},
       URL = {https://doi.org/10.1016/j.jcta.2015.03.012},
}


@article {proofofshuffle,
    AUTHOR = {Carlsson, Erik and Mellit, Anton},
     TITLE = {A proof of the shuffle conjecture},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {31},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {661--697},
   MRCLASS = {05E10 (05E05 33D52)},
  MRNUMBER = {3787405},
MRREVIEWER = {Tanja\ Stojadinovi\'c},
       DOI = {10.1090/jams/893},
       URL = {https://doi.org/10.1090/jams/893},
}


@book {MR2371044,
    AUTHOR = {Haglund, James},
     TITLE = {The {$q$},{$t$}-{C}atalan numbers and the space of diagonal
              harmonics},
    SERIES = {University Lecture Series},
    VOLUME = {41},
      NOTE = {With an appendix on the combinatorics of Macdonald
              polynomials},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2008},
     PAGES = {viii+167},
      ISBN = {978-0-8218-4411-3; 0-8218-4411-3},
   MRCLASS = {05E05 (05A05 05A30 33D52)},
  MRNUMBER = {2371044},
MRREVIEWER = {Michael\ A.\ Zabrocki},
       DOI = {10.1007/s10711-008-9270-0},
       URL = {https://doi.org/10.1007/s10711-008-9270-0},
}



@article {GarsiaHaiman,
    AUTHOR = {Garsia, A. M. and Haiman, M.},
     TITLE = {A remarkable {$q,t$}-{C}atalan sequence and {$q$}-{L}agrange
              inversion},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {5},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {191--244},
MRREVIEWER = {Edward\ E.\ Allen},
       DOI = {10.1023/A:1022476211638},
       URL = {https://doi.org/10.1023/A:1022476211638},
}


@article {HaimanDH,
    AUTHOR = {Haiman, Mark D.},
     TITLE = {Conjectures on the quotient ring by diagonal invariants},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {3},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {17--76},
       DOI = {10.1023/A:1022450120589},
       URL = {https://doi.org/10.1023/A:1022450120589},
}




@article{haglund,
title = {A conjectured combinatorial formula for the Hilbert series for diagonal harmonics},
journal = {Discrete Mathematics},
volume = {298},
number = {1},
pages = {189-204},
year = {2005},
note = {Formal Power Series and Algebraic Combinatorics 2002 (FPSAC'02)},
doi = {https://doi.org/10.1016/j.disc.2004.01.022},
url = {https://www.sciencedirect.com/science/article/pii/S0012365X05002402},
author = {J. Haglund and N. Loehr},
keywords = {Catalan number, Parking functions, Labelled trees, Hilbert series},
abstract = {We introduce a conjectured way of expressing the Hilbert series of diagonal harmonics as a weighted sum over parking functions. Our conjecture is based on a pair of statistics for the q,t-Catalan sequence discovered by Haiman and proven by Haglund and Garsia (Proc. Nat. Acad. Sci. 98 (2001) 4313–4316). We show how our q,t-parking function formula for the Hilbert series can be expressed more compactly as a sum over permutations. We also derive two equivalent forms of our conjecture, one of which is based on the original pair of statistics for the q,t-Catalan introduced by Haglund and the other of which is expressed in terms of rooted, labelled trees.}
}




@article{Pyke,
    AUTHOR = {Pyke, Ronald},
     TITLE = {The supremum and infimum of the {P},oisson process},
   JOURNAL = {Ann. Math. Statist.},
  FJOURNAL = {Annals of Mathematical Statistics},
    VOLUME = {30},
      YEAR = {1959},
     PAGES = {568--576},
   MRCLASS = {60.00},
  MRNUMBER = {107315},
MRREVIEWER = {Z. W. Birnbaum},
},


@misc{callan_bijections_2021,
	title = {Some bijections for lattice paths},
	url = {http://arxiv.org/abs/2112.05241},
	doi = {10.48550/arXiv.2112.05241},
	abstract = {We present three bijections, the first between little Schr{\textbackslash}"\{o\}der paths and a class of growth-constrained integer sequences, the second between lattice paths consisting of steps with nonnegative slope and another class of growth-constrained sequences, the third between a class of lattice paths with steps \$(1,1)\$ and \$(1,-j{\textbackslash},),{\textbackslash} j{\textbackslash}ge 1\$, and a class with steps \$(k,1),{\textbackslash} k{\textbackslash}ge 1\$, and \$(1,-1)\$.},
	urldate = {2024-08-10},
	author = {Callan, David},
	month = dec,
	year = {2021},
	note = {arXiv:2112.05241 [math]},
	keywords = {Mathematics - Combinatorics, 05A15},
	file = {Callan - 2021 - Some bijections for lattice paths.pdf:/Users/kylecelano/Zotero/storage/FK88SF99/Callan - 2021 - Some bijections for lattice paths.pdf:application/pdf},
}

@article{rawlings_euler-catalan_1988,
	title = {The {Euler}-{Catalan} {Identity}},
	volume = {9},
	url = {https://www.sciencedirect.com/science/article/pii/S0195669888800271},
	doi = {10.1016/S0195-6698(88)80027-1},
	abstract = {The enumeration of permutations by descents, major index, inversion number, and certain three letter patterns leads to a multivariable recurrence relationship which simultaneously contains generalizations of both the Catalan and Eulerian numbers.},
	number = {1},
	urldate = {2024-10-10},
	journal = {European Journal of Combinatorics},
	author = {Rawlings, Don},
	month = jan,
	year = {1988},
	pages = {53--60},
	file = {Rawlings - 1988 - The Euler-Catalan Identity.pdf:/Users/kylecelano/Zotero/storage/ZNB3YCAF/Rawlings - 1988 - The Euler-Catalan Identity.pdf:application/pdf;ScienceDirect Snapshot:/Users/kylecelano/Zotero/storage/G7P9ZWHM/S0195669888800271.html:text/html},
}

@article{bib:Carlson+,
    AUTHOR = {Carlson, Joshua and Christensen, Alex and Harris, Pamela E.
              and Jones, Zakiya and Ramos Rodr\'iguez, Andr\'es},
     TITLE = {Parking functions: choose your own adventure},
   JOURNAL = {College Math. J.},
  FJOURNAL = {The College Mathematics Journal},
    VOLUME = {52},
      YEAR = {2021},
    NUMBER = {4},
     PAGES = {254--264},
       DOI = {10.1080/07468342.2021.1943115},
       URL = {https://doi.org/10.1080/07468342.2021.1943115},
}

@article{bousquet-melou_sorted_2000,
	series = {{FPSAC}'98},
	title = {Sorted and/or sortable permutations},
	volume = {225},
	url = {https://www.sciencedirect.com/science/article/pii/S0012365X00001461},
	doi = {10.1016/S0012-365X(00)00146-1},
	abstract = {In his Ph.D. thesis, Julian West (Permutations with restricted subsequences and stack-sortable permutations, MIT, 1990) studied in depth a map Π that acts on permutations of the symmetric group Sn by partially sorting them through a stack. The main motivation of this paper is to characterize and count the permutations of Π(Sn), which we call sorted permutations. This is equivalent to counting preorders of increasing binary trees. We first find a local characterization of sorted permutations. Then, using an extension of Zeilberger's factorization of two-stack sortable permutations (D. Zeilberger, Discrete Math. 102 (1992) 85–93), we obtain for the generating function of sorted permutations an unusual functional equation. Out of curiosity, we apply the same treatment to four other families of permutations (general permutations, one-stack sortable permutations, two-stack sortable permutations, sorted and sortable permutations) and compare the functional equations we obtain. All of them have similar features, involving a divided difference. Moreover, most of them have interesting q-analogs obtained by counting inversions. We solve (some of) our equations.},
	number = {1},
	urldate = {2024-10-10},
	journal = {Discrete Mathematics},
	author = {Bousquet-Mélou, Mireille},
	month = oct,
	year = {2000},
	pages = {25--50},
	file = {Bousquet-Mélou - 2000 - Sorted andor sortable permutations.pdf:/Users/kylecelano/Zotero/storage/L6EHWEDQ/Bousquet-Mélou - 2000 - Sorted andor sortable permutations.pdf:application/pdf;ScienceDirect Snapshot:/Users/kylecelano/Zotero/storage/6Y9MZUWU/S0012365X00001461.html:text/html},
}

@article{defant_stack-sorting_2022,
	title = {Stack-{Sorting} and {Beyond}},
	url = {https://dataspace.princeton.edu/handle/88435/dsp016m311s469},
	abstract = {In 1990, West initiated an extensive investigation of the stack-sorting map, a deterministic version of Knuth's stack-sorting machine that acts on permutations. At first sight, this map appears complicated and messy; for many years, it was studied as an isolated topic without many connections to other parts of mathematics. One of the primary goals of this thesis is to demonstrate that the stack-sorting map is actually a very natural object of study with fascinating connections to other mathematical areas. Throughout our exploration of the stack-sorting map, we will encounter cumulants in noncommutative probability theory; special convex polytopes called {\textbackslash}emph\{fertilitopes\}; intervals in special posets; binary plane trees; several questions about symmetry, unimodality, log-concavity, and real-rootedness; and many interesting combinatorial sequences. We will also formulate natural generalizations of stack-sorting for arbitrary Coxeter groups. The new techniques that we introduce will allow us to answer several old questions, reprove and generalize known results, prove completely new theorems, and formulate entirely new questions.
      Much of our attention will be directed toward {\textbackslash}emph\{valid hook configurations\}, which are new combinatorial objects that allow us to count the preimages of an arbitrary permutation under the stack-sorting map. Very surprisingly, valid hook configurations also arise in a formula in noncommutative probability theory that converts from free cumulants to classical cumulants. This allows us to use free probability theory to prove deep facts about the stack-sorting map and its generalizations. We also initiate a theory of {\textbackslash}emph\{troupes\}, which are sets of colored binary plane trees that are closed under certain operations. Troupes provide a broad framework where many results about stack-sorting can be generalized uniformly. On the other hand, we will also show how stack-sorting and its generalizations can be used, along with troupes and valid hook configurations, to prove a striking relationship between free and classical cumulants. Troupes and valid hook configurations help to illuminate the delightful combinatorial structure lurking beneath the surface of the stack-sorting map; our hope is that some readers will see this hidden structure, find inspiration to answer some of the new questions that we formulate, and ask new questions of their own.},
	language = {en},
	urldate = {2024-10-10},
	author = {Defant, Colin},
	year = {2022},
	note = {Accepted: 2022-06-16T20:34:02Z
Publisher: Princeton, NJ : Princeton University},
}
@article{WEST1993303,
title = {Sorting twice through a stack},
journal = {Theoretical Computer Science},
volume = {117},
number = {1},
pages = {303-313},
year = {1993},
doi = {https://doi.org/10.1016/0304-3975(93)90321-J},
url = {https://www.sciencedirect.com/science/article/pii/030439759390321J},
author = {Julian West},
abstract = {We consider the operation of stack-sorting studied by Knuth. We take the point of view that stack-sorting is a function mapping permutations to permutations, and consider those n-permutations which are sorted by k iterations of this function. Some results are: that all n-permutations are sorted after n − 1 iterations, that (n − 2)! actually require n − 1 iterations, and that a further 72(n − 2)! + (n − 3)! require n − 2 iterations. It has long been known that the permutations sorted after one iteration are the wedge-free permutations, which are counted by the Catalan number (2n)!⧸(n!(n + 1)!). The permutations sorted after two iterations are characterized, and their number conjectured to be 2(3n)!⧸((n + 1)!(2n + 1)!).}
}

@book{knuth1997art,
  title={The Art of Computer Programming, volume 1 Fundamental Algorithms},
  author={Knuth, Donald E},
  year={1997},
  publisher={Addison Wesley Longman Publishing Co., Inc.}
}

@article{carlitz1933,
 ISSN = {00029947, 10886850},
 URL = {http://www.jstor.org/stable/1989316},
 author = {Leonard Carlitz},
 journal = {Transactions of the American Mathematical Society},
 number = {1},
 pages = {122--136},
 publisher = {American Mathematical Society},
 title = {On Abelian Fields},
 urldate = {2024-10-14},
 volume = {35},
 year = {1933}
}

@article{carlitz1948,
author = {L. Carlitz},
title = {{$q$-Bernoulli numbers and polynomials}},
volume = {15},
journal = {Duke Mathematical Journal},
number = {4},
publisher = {Duke University Press},
pages = {987 -- 1000},
year = {1948},
doi = {10.1215/S0012-7094-48-01588-9},
URL = {https://doi.org/10.1215/S0012-7094-48-01588-9}
}

@article{gould1961,
author = {H. W. Gould},
title = {{The $q$-Stirling numbers of first and second kinds}},
volume = {28},
journal = {Duke Mathematical Journal},
number = {2},
publisher = {Duke University Press},
pages = {281 -- 289},
year = {1961},
doi = {10.1215/S0012-7094-61-02826-5},
URL = {https://doi.org/10.1215/S0012-7094-61-02826-5}
}

@article{SAGAN199169,
title = {A maj Statistic for Set Partitions},
journal = {European Journal of Combinatorics},
volume = {12},
number = {1},
pages = {69-79},
year = {1991},
doi = {https://doi.org/10.1016/S0195-6698(13)80009-1},
url = {https://www.sciencedirect.com/science/article/pii/S0195669813800091},
author = {Bruce E. Sagan},
abstract = {We propose a weighting of set partitions which is analogous to the major index for permutations. The corresponding weight generating function yields the q-Stirling numbers of the second kind of Carlitz and Gould. Other interpretations of maj are given in terms of restricted growth functions, rook placements and reduced matrices. The Foata bijection interchanging inv and maj for permutations also has a version for partitions. Finally, we generalize these constructions to an analog of Rawling's rmaj and to two new kinds of p, q-Stirling numbers.}
}

@book{macdonald1998symmetric,
  title={Symmetric functions and {H}all polynomials},
  author={Macdonald, I. G.},
  year={1998},
  publisher={Oxford University Press}
}

@book{sagan2013symmetric,
    AUTHOR = {Sagan, Bruce E.},
     TITLE = {The symmetric group},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {203},
   EDITION = {Second},
      NOTE = {Representations, combinatorial algorithms, and symmetric
              functions},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2001},
     PAGES = {xvi+238},
       DOI = {10.1007/978-1-4757-6804-6},
       URL = {https://doi.org/10.1007/978-1-4757-6804-6},
}

@article{cayley1856,
author = {A. Cayley},
title = {LVIII. On the analytical forms called trees.-Part II},
JOURNAL = {Philos. Mag. (4)},
  FJOURNAL = {The London, Edinburgh, and Dublin Philosophical Magazine and
              Journal of Sciences. Fourth Series},
volume = {18},
number = {121},
pages = {374--378},
year = {1859},
publisher = {Taylor \& Francis},
doi = {10.1080/14786445908642782},
}