%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/


%% Created for Nick Beaton at 2016-09-24 13:54:23 -0600 


%% Saved with string encoding Unicode (UTF-8) 

@article{Mac88,
  title={A new class of symmetric functions.},
  author={Macdonald, Ian G.},
  journal={S{\'e}minaire Lotharingien de Combinatoire},
  volume={20},
  pages={B20a--41},
  year={1988},
  publisher={Universit{\"a}t Wien, Fakult{\"a}t f{\"u}r Mathematik}
}

@article{DM08,
  title={Factorization formulas for Macdonald polynomials},
  author={Descouens, Fran{\c{c}}ois and Morita, Hideaki},
  journal={European Journal of Combinatorics},
  volume={29},
  number={2},
  pages={395--410},
  year={2008},
  publisher={Elsevier}
}
@article{HHL05,
  title={A combinatorial formula for {M}acdonald polynomials},
  author={Haglund, Jim and Haiman, Mark and Loehr, Nick},
  journal={Journal of the American Mathematical Society},
  volume={18},
  number={3},
  pages={735--761},
  year={2005}
}

@article{BMPS19,
  title={Catalan functions and $k$-Schur positivity},
  author={Blasiak, Jonah and Morse, Jennifer and Pun, Anna and Summers, Daniel},
  journal={Journal of the American Mathematical Society},
  volume={32},
  number={4},
  pages={921--963},
  year={2019}
}

@article{Tom21,
  title={A horizontal-strip {LLT} polynomial is determined by its weighted graph},
  author={Tom, Foster},
  journal={arXiv:2110.07984},
  year={2021}
}

@unpublished{KLO23+,
    title={Shuffle formula in Science Fiction for Macdonald polynomials},
    author = {Kim, Donghyun and Lee, Seung Jin and Oh, Jaeseong},
    note = {in preparation},
}

@article{But94,
  title={Subgroup lattices and symmetric functions},
  author={Butler, Lynne},
  journal={Memoirs of the American Mathematical Society},
  year={1994}
}

@article{AS17,
  title={A major-index preserving map on fillings},
  author={Alexandersson, Per and Sawhney, Mehtaab},
  journal={The Electronic Journal of Combinatorics},
  volume={24},
  number={4},
  pages={P4--3},
  year={2017}
}

@article{HHL08,
  title={A combinatorial formula for nonsymmetric Macdonald polynomials},
  author={Haglund, James and Haiman, Mark and Loehr, Nick},
  journal={American Journal of Mathematics},
  volume={130},
  number={2},
  pages={359--383},
  year={2008},
  publisher={Johns Hopkins University Press}
}

@article{Zab98,
  title={A Macdonald vertex operator and standard tableaux statistics},
  author={Zabrocki, Mike},
  journal={The Electronic Journal of Combinatorics},
  pages={R45},
  year={1998}
}

@article{GH93,
  title={A graded representation model for {M}acdonald's polynomials.},
  author={Garsia, Adriano M and Haiman, Mark},
  journal={Proceedings of the National Academy of Sciences},
  volume={90},
  number={8},
  pages={3607--3610},
  year={1993},
  publisher={National Acad Sciences}
}


@article{SW85,
  title={A {S}chensted algorithm for rim hook tableaux},
  author={Stanton, Dennis W and White, Dennis E},
  journal={Journal of Combinatorial Theory, Series A},
  volume={40},
  number={2},
  pages={211--247},
  year={1985},
  publisher={Elsevier}
}


@article{GHQR19,
  title={$ e $-Positivity Results and Conjectures},
  author={Garsia, Adriano M and Haglund, James and Qiu, Dun and Romero, Marino},
  journal={arXiv preprint arXiv:1904.07912},
  year={2019}
}
@article{HHLRU05,
  title={A combinatorial formula for the character of the diagonal coinvariants},
  author={Haglund, James and Haiman, Mark and Loehr, Nicholas and Remmel, Jeffrey B and Ulyanov, Alexander},
  journal={Duke Mathematical Journal},
  volume={126},
  number={2},
  pages={195--232},
  year={2005},
  publisher={Duke University Press}
}
@article{BG99,
  title={Science Fiction and {M}acdonald’s polynomials},
  author={Bergeron, Francois and Garsia, Adriano M},
  journal={CRM Proceedings \& Lecture Notes, American Mathematical Society},
  volume={22},
  pages={1--52},
  year={1999}
}

@article{GH07,
  title={Affine {H}ecke algebras and positivity of {LLT} and {M}acdonald polynomials},
  author={Grojnowski, Ian and Haiman, Mark},
  journal={preprint},
  year={2007}
}

@article{Ass18,
  title={Toward the Schur expansion of {M}acdonald polynomials},
  author={Assaf, Sami},
  journal={The Electronic Journal of Combinatorics},
  volume={25},
  number={2},
  pages={2--44},
  year={2018}
}

@article{AS22,
  title={A combinatorial expansion of vertical-strip {LLT} polynomials in the basis of elementary symmetric functions},
  author={Alexandersson, Per and Sulzgruber, Robin},
  journal={Advances in Mathematics},
  volume={400},
  pages={108256},
  year={2022},
  publisher={Elsevier}
}

@article{Arm22,
  title={A proof of the $\frac{n!}{2}$ conjecture for hook shapes},
  author={Armon, Sam},
  journal={Annals of Combinatorics},
  pages={1--14},
  year={2022},
  publisher={Springer}
}

@article{Hai02,
  title={Vanishing theorems and character formulas for the Hilbert scheme of points in the plane},
  author={Haiman, Mark},
  journal={Inventiones mathematicae},
  volume={149},
  pages={371--407},
  year={2002},
  publisher={Springer}
}

@article{Hai01,
  title={Hilbert schemes, polygraphs and the {M}acdonald positivity conjecture},
  author={Haiman, Mark},
  journal={Journal of the American Mathematical Society},
  volume={14},
  number={4},
  pages={941--1006},
  year={2001}
}


@article{LLT97,
  title={Ribbon tableaux, {H}all--{L}ittlewood functions, quantum affine algebras, and unipotent varieties},
  author={Lascoux, Alain and Leclerc, Bernard and Thibon, Jean-Yves},
  journal={Journal of Mathematical Physics},
  volume={38},
  number={2},
  pages={1041--1068},
  year={1997},
  publisher={American Institute of Physics}
}


@article{HNY20,
  title={Melting lollipop chromatic quasisymmetric functions and {S}chur expansion of unicellular {LLT} polynomials},
  author={Huh, JiSun and Nam, Sun-Young and Yoo, Meesue},
  journal={Discrete Mathematics},
  volume={343},
  number={3},
  pages={111728},
  year={2020},
  publisher={Elsevier}
}

@article{Lee21,
  title={Linear relations on {LLT} polynomials and their $k$-{S}chur positivity for $k= 2$},
  author={Lee, Seung Jin},
  journal={Journal of Algebraic Combinatorics},
  volume={53},
  number={4},
  pages={973--990},
  year={2021},
  publisher={Springer}
} 

@phdthesis{Mil19,
  title={On the $k$-{S}chur Positivity of $k$-Bandwidth {LLT} Polynomials},
  author={Miller, Christopher R.},
  year={2019},
  school={UC Berkeley}
}

@article{LLM03,
  title={Tableau atoms and a new {M}acdonald positivity conjecture},
  author={Lapointe, Luc and Lascoux, Alain and Morse, Jennifer},
  journal={Duke Mathematical Journal},
  volume={116},
  number={1},
  pages={103--146},
  year={2003},
  publisher={Duke University Press}
}

@article{Lam08,
  title={Schubert polynomials for the affine {G}rassmannian},
  author={Lam, Thomas},
  journal={Journal of the American Mathematical Society},
  volume={21},
  number={1},
  pages={259--281},
  year={2008}
}

@article{LM07,
  title={A $k$-tableau characterization of $k$-{S}chur functions},
  author={Lapointe, Luc and Morse, Jennifer},
  journal={Advances in mathematics},
  volume={213},
  number={1},
  pages={183--204},
  year={2007},
  publisher={Elsevier}
}

@article{LM08,
  title={Quantum cohomology and the $k$-{S}chur basis},
  author={Lapointe, Luc and Morse, Jennifer},
  journal={Transactions of the American Mathematical Society},
  volume={360},
  number={4},
  pages={2021--2040},
  year={2008}
}

@article{LM05,
  title={Tableaux on $k+1$-cores, reduced words for affine permutations, and $k$-Schur expansions},
  author={Lapointe, Luc and Morse, Jennifer},
  journal={Journal of Combinatorial Theory, Series A},
  volume={112},
  number={1},
  pages={44--81},
  year={2005},
  publisher={Elsevier}
}

@article{Jin91,
  title={Vertex operators and Hall-Littlewood symmetric functions},
  author={Jing, Naihuan},
  journal={Advances in Mathematics},
  volume={87},
  number={2},
  pages={226--248},
  year={1991},
  publisher={Elsevier}
}

@article{SZ01,
  title={Hall--Littlewood vertex operators and generalized Kostka polynomials},
  author={Shimozono, Mark and Zabrocki, Mike},
  journal={Advances in Mathematics},
  volume={158},
  number={1},
  pages={66--85},
  year={2001},
  publisher={Elsevier}
}

@article{LOR23,
  title={Haglund's conjecture for multi-$t$ {M}acdonald polynomials},
  author={Lee, Seung Jin and Oh, Jaeseong and Rhoades, Brendon},
  journal={Discrete Mathematics},
  volume={346},
  number={6},
  pages={113360},
  year={2023},
  publisher={Elsevier}
}

@book{Mac98,
  title={Symmetric functions and Hall polynomials},
  author={Macdonald, Ian Grant},
  year={1998},
  publisher={Oxford university press}
}

@article{Ges84,
  title={Multipartite P-partitions and inner products of skew Schur functions},
  author={Gessel, Ira M},
  journal={Contemp. Math},
  volume={34},
  number={289-301},
  pages={101},
  year={1984}
}


@article{CM18,
  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}
}