@article{remmel1984multiplying,
    AUTHOR = {Remmel, J. B. and Whitney, R.},
     TITLE = {Multiplying {S}chur functions},
   JOURNAL = {J. Algorithms},
  FJOURNAL = {Journal of Algorithms},
    VOLUME = {5},
      YEAR = {1984},
    NUMBER = {4},
     PAGES = {471--487},
      ISSN = {0196-6774},
   MRCLASS = {20C30 (05A17)},
  MRNUMBER = {769977},
MRREVIEWER = {J.\ D\'esarm\'enien},
       DOI = {10.1016/0196-6774(84)90002-6},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/0196-6774(84)90002-6},
}


@article{littlewood1934group,
  title={Group characters and algebra},
  author={Littlewood, Dudley Ernest and Richardson, Archibald Read},
  journal={Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character},
  volume={233},
  number={721-730},
  pages={99--141},
  year={1934},
  publisher={The Royal Society London}
}


@article{zelevinsky1981generalization,
    AUTHOR = {Zelevinsky, A. V.},
     TITLE = {A generalization of the {L}ittlewood-{R}ichardson rule and the
              {R}obinson-{S}chensted-{K}nuth correspondence},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {69},
      YEAR = {1981},
    NUMBER = {1},
     PAGES = {82--94},
      ISSN = {0021-8693},
   MRCLASS = {20C30 (05A17)},
  MRNUMBER = {613858},
MRREVIEWER = {Michael\ H.\ Peel},
       DOI = {10.1016/0021-8693(81)90128-9},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/0021-8693(81)90128-9},
}


@article{berenstein1992triple,
    AUTHOR = {Berenstein, A. D. and Zelevinsky, A. V.},
     TITLE = {Triple multiplicities for {${\rm sl}(r+1)$} and the spectrum
              of the exterior algebra of the adjoint representation},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {1},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {7--22},
      ISSN = {0925-9899,1572-9192},
   MRCLASS = {17B10},
  MRNUMBER = {1162639},
MRREVIEWER = {Dao\ Ji\ Meng},
       DOI = {10.1023/A:1022429213282},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1023/A:1022429213282},
}

@article{berenstein1999tensor,
      title={Tensor product multiplicities, canonical bases and totally positive varieties}, 
      author={Arkady Berenstein and Andrei Zelevinsky},
      year={1999},
      eprint={math/9912012},
      archivePrefix={arXiv},
      primaryClass={math.RT},
}


@article{knutson1999honeycomb,
    AUTHOR = {Knutson, Allen and Tao, Terence},
     TITLE = {The honeycomb model of {${\rm GL}_n({\bf C})$} tensor
              products. {I}. {P}roof of the saturation conjecture},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {12},
      YEAR = {1999},
    NUMBER = {4},
     PAGES = {1055--1090},
      ISSN = {0894-0347,1088-6834},
   MRCLASS = {20G05 (05E05 14M15 52B20)},
  MRNUMBER = {1671451},
MRREVIEWER = {Anders\ Skovsted\ Buch},
       DOI = {10.1090/S0894-0347-99-00299-4},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1090/S0894-0347-99-00299-4},
}


@article{reiner1998percentage,
    AUTHOR = {Reiner, Victor and Shimozono, Mark},
     TITLE = {Percentage-avoiding, northwest shapes and peelable tableaux},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {82},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {1--73},
      ISSN = {0097-3165,1096-0899},
   MRCLASS = {05E15 (05E05 05E10)},
  MRNUMBER = {1616579},
MRREVIEWER = {Witold\ Kra\'skiewicz},
       DOI = {10.1006/jcta.1997.2841},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1006/jcta.1997.2841},
}


@article{lam2007schur,
    AUTHOR = {Lam, Thomas and Postnikov, Alexander and Pylyavskyy, Pavlo},
     TITLE = {Schur positivity and {S}chur log-concavity},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {129},
      YEAR = {2007},
    NUMBER = {6},
     PAGES = {1611--1622},
      ISSN = {0002-9327,1080-6377},
   MRCLASS = {05E05},
  MRNUMBER = {2369890},
MRREVIEWER = {Riccardo\ Biagioli},
       DOI = {10.1353/ajm.2007.0045},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1353/ajm.2007.0045},
}



@article{lam2007alcoved,
  title={Alcoved polytopes, {I}},
  author={Lam, Thomas and Postnikov, Alexander},
  journal={Discrete \& Computational Geometry},
  volume={38},
  pages={453--478},
  year={2007},
  publisher={Springer}
}



@article{lam2018alcoved,
  title={Alcoved polytopes {II}},
  author={Lam, Thomas and Postnikov, Alexander},
  journal={Lie Groups, Geometry, and Representation Theory: A Tribute to the Life and Work of Bertram Kostant},
  pages={253--272},
  year={2018},
  publisher={Springer}
}


@article{dobrovolska2007products,
    AUTHOR = {Dobrovolska, Galyna and Pylyavskyy, Pavlo},
     TITLE = {On products of {$\mathfrak{sl}_{\mathfrak n}$} characters and support
              containment},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {316},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {706--714},
      ISSN = {0021-8693,1090-266X},
   MRCLASS = {17B10},
  MRNUMBER = {2358610},
MRREVIEWER = {Timo\ Neuvonen},
       DOI = {10.1016/j.jalgebra.2006.10.033},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/j.jalgebra.2006.10.033},
}

@article{nguyen2025temperley,
    AUTHOR = {Nguyen, Son and Pylyavskyy, Pavlo},
     TITLE = {Temperley-{L}ieb crystals},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2025},
    NUMBER = {7},
     PAGES = {Paper No. rnaf080, 28},
      ISSN = {1073-7928,1687-0247},
   MRCLASS = {05E10 (20C08)},
  MRNUMBER = {4887473},
MRREVIEWER = {H.\ H.\ Andersen},
       DOI = {10.1093/imrn/rnaf080},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1093/imrn/rnaf080},
}

@article{reiner1995key,
  title={Key polynomials and a flagged {L}ittlewood—{R}ichardson rule},
  author={Reiner, Victor and Shimozono, Mark},
  journal={Journal of Combinatorial Theory, Series A},
  volume={70},
  number={1},
  pages={107--143},
  year={1995},
  publisher={Elsevier}
}



@inproceedings{demazure1974desingularisation,
  title={D{\'e}singularisation des vari{\'e}t{\'e}s de {S}chubert g{\'e}n{\'e}ralis{\'e}es},
  author={Demazure, Michel},
  booktitle={Annales scientifiques de l'{\'E}cole normale sup{\'e}rieure},
  volume={7},
  pages={53--88},
  year={1974}
}



@article{demazure1974nouvelle,
  title={Une nouvelle formule des caracteres},
  author={Demazure, Michel},
  journal={Bull. Sci. Math},
  volume={2},
  number={98},
  pages={163--172},
  year={1974}
}



@article{lascoux1983,
  title={Geom{\'e}trie alg{\'e}brique-polyn{\'o}mes de Schubert},
  author={Lascoux, Alain and Schlltzenberger, Marcel-Paul},
  journal={C. R. Acad. Sci. Paris},
  number={294},
  pages={447--450},
  year={1982}
}


@article{lascoux1990keys,
  title={Keys \& standard bases},
  author={Lascoux, Alain and Schlltzenberger, Marcel-Paul},
  journal={Institute for Mathematics and Its Applications},
  volume={19},
  pages={125},
  year={1990}
}


@article{lascoux1989tableaux,
  title={Tableaux and noncommutative {S}chubert polynomials},
  author={Lascoux, Alain and Sch{\"u}tzenberger, Marcel-Paul},
  journal={Functional Analysis and Its Applications},
  volume={23},
  number={3},
  pages={223--225},
  year={1989},
  publisher={Springer}
}


@phdthesis{kohnert2006weintrauben,
  title={Weintrauben, polynome, tableaux},
  author={Kohnert, Axel},
  year={2006}
}



@article{wachs1985flagged,
  title={Flagged {S}chur functions, {S}chubert polynomials, and symmetrizing operators},
  author={Wachs, Michelle L},
  journal={Journal of Combinatorial Theory, Series A},
  volume={40},
  number={2},
  pages={276--289},
  year={1985},
  publisher={Elsevier}
}


@article{magyar1998schubert,
  title={Schubert polynomials and Bott-Samelson varieties},
  author={Magyar, Peter},
  journal={Commentarii Mathematici Helvetici},
  volume={73},
  pages={603--636},
  year={1998},
  publisher={Springer}
}



@article{gessel1989determinants,
  title={Determinants, paths, and plane partitions},
  author={Gessel, Ira M and Viennot, Xavier},
  journal={preprint},
  volume={132},
  number={197.15},
  year={1989}
}



@article{bergeron2004some,
      title={Some positive differences of products of Schur functions}, 
      author={Francois Bergeron and Peter McNamara},
      year={2004},
      eprint={math/0412289},
      archivePrefix={arXiv},
      primaryClass={math.CO},
}


@article{fomin2005eigenvalues,
    AUTHOR = {Fomin, Sergey and Fulton, William and Li, Chi-Kwong and Poon,
              Yiu-Tung},
     TITLE = {Eigenvalues, singular values, and {L}ittlewood-{R}ichardson
              coefficients},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {127},
      YEAR = {2005},
    NUMBER = {1},
     PAGES = {101--127},
      ISSN = {0002-9327,1080-6377},
   MRCLASS = {05E15 (14M15 15A18)},
  MRNUMBER = {2115662},
MRREVIEWER = {Marc\ A. A. van Leeuwen},
      DOI = {10.1353/ajm.2005.0005}
}


@article{lascoux1997ribbon,
    AUTHOR = {Lascoux, Alain and Leclerc, Bernard and Thibon, Jean-Yves},
     TITLE = {Ribbon tableaux, {H}all-{L}ittlewood functions, quantum affine
              algebras, and unipotent varieties},
   JOURNAL = {J. Math. Phys.},
  FJOURNAL = {Journal of Mathematical Physics},
    VOLUME = {38},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {1041--1068},
      ISSN = {0022-2488,1089-7658},
   MRCLASS = {05E10 (05E05 33D80 81R10)},
  MRNUMBER = {1434225},
MRREVIEWER = {Thomas\ Scharf},
       DOI = {10.1063/1.531807},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1063/1.531807},
}

@article{okounkov1997log,
    AUTHOR = {Okounkov, Andrei},
     TITLE = {Log-concavity of multiplicities with application to characters
              of {${\rm U}(\infty)$}},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {127},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {258--282},
      ISSN = {0001-8708,1090-2082},
   MRCLASS = {22E46 (05A20 05E15 22E65)},
  MRNUMBER = {1448715},
MRREVIEWER = {David\ K.\ Maslen},
       DOI = {10.1006/aima.1997.1622},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1006/aima.1997.1622},
}


@phdthesis{pylyavskyy2007comparing,
  title={Comparing products of {S}chur functions and quasisymmetric functions},
  author={Pylyavskyy, Pavlo},
  year={2007},
  school={Massachusetts Institute of Technology}
}



@article{assaf2019pieri,
  title={A {P}ieri rule for {D}emazure characters of the general linear group},
  author={Assaf, Sami and Quijada, Danjoseph},
  journal={arXiv preprint arXiv:1908.08502},
  year={2019}
}



@article{rhoades2005temperley,
    AUTHOR = {Rhoades, Brendon and Skandera, Mark},
     TITLE = {Temperley-{L}ieb immanants},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {9},
      YEAR = {2005},
    NUMBER = {4},
     PAGES = {451--494},
      ISSN = {0218-0006,0219-3094},
   MRCLASS = {20C08 (05E15 15A15)},
  MRNUMBER = {2205034},
MRREVIEWER = {Alessio\ Del Padrone},
       DOI = {10.1007/s00026-005-0268-0},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1007/s00026-005-0268-0},
}



@article{rhoades2006kazhdan,
    AUTHOR = {Rhoades, Brendon and Skandera, Mark},
     TITLE = {Kazhdan-{L}usztig immanants and products of matrix minors},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {304},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {793--811},
      ISSN = {0021-8693,1090-266X},
   MRCLASS = {20C08 (05E05 15A15)},
  MRNUMBER = {2264279},
MRREVIEWER = {Gregory\ S.\ Warrington},
       DOI = {10.1016/j.jalgebra.2005.07.017},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/j.jalgebra.2005.07.017},
}



@article{haiman1993hecke,
    AUTHOR = {Haiman, Mark},
     TITLE = {Hecke algebra characters and immanant conjectures},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {6},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {569--595},
      ISSN = {0894-0347,1088-6834},
   MRCLASS = {05E05 (14M15 20C30 20F55)},
  MRNUMBER = {1186961},
MRREVIEWER = {James\ E.\ Humphreys},
       DOI = {10.2307/2152777},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.2307/2152777},
}


@article{lusztig1990canonical,
    AUTHOR = {Lusztig, G.},
     TITLE = {Canonical bases arising from quantized enveloping algebras},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {3},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {447--498},
      ISSN = {0894-0347,1088-6834},
   MRCLASS = {17B35 (16A64)},
  MRNUMBER = {1035415},
MRREVIEWER = {Ya.\ S.\ So\u ibel\cprime man},
       DOI = {10.2307/1990961},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.2307/1990961},
}


@article{kashiwara1991crystal,
    AUTHOR = {Kashiwara, M.},
     TITLE = {On crystal bases of the {$Q$}-analogue of universal enveloping
              algebras},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {63},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {465--516},
      ISSN = {0012-7094,1547-7398},
   MRCLASS = {17B37 (17B10 17B67)},
  MRNUMBER = {1115118},
MRREVIEWER = {Kailash\ C.\ Misra},
       DOI = {10.1215/S0012-7094-91-06321-0},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1215/S0012-7094-91-06321-0},
}

@article{fomin2002cluster,
    AUTHOR = {Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Cluster algebras. {I}. {F}oundations},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {15},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {497--529},
      ISSN = {0894-0347,1088-6834},
   MRCLASS = {16S99 (14M99 17B99)},
  MRNUMBER = {1887642},
MRREVIEWER = {Eric\ N.\ Sommers},
       DOI = {10.1090/S0894-0347-01-00385-X},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1090/S0894-0347-01-00385-X},
}

@article{kashiwara1993global,
    AUTHOR = {Kashiwara, Masaki},
     TITLE = {Global crystal bases of quantum groups},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {69},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {455--485},
      ISSN = {0012-7094,1547-7398},
   MRCLASS = {17B37 (17B10 81R50)},
  MRNUMBER = {1203234},
MRREVIEWER = {Kailash\ C.\ Misra},
       DOI = {10.1215/S0012-7094-93-06920-7},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1215/S0012-7094-93-06920-7},
}

@article{berenstein1996parametrizations,
    AUTHOR = {Berenstein, Arkady and Fomin, Sergey and Zelevinsky, Andrei},
     TITLE = {Parametrizations of canonical bases and totally positive
              matrices},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {122},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {49--149},
      ISSN = {0001-8708,1090-2082},
   MRCLASS = {17B37 (05E15 20G05)},
  MRNUMBER = {1405449},
MRREVIEWER = {Kailash\ C.\ Misra},
       DOI = {10.1006/aima.1996.0057},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1006/aima.1996.0057},
}


@article{du1992canonical,
    AUTHOR = {Du, Jie},
     TITLE = {Canonical bases for irreducible representations of quantum
              {${\rm GL}_n$}},
   JOURNAL = {Bull. London Math. Soc.},
  FJOURNAL = {The Bulletin of the London Mathematical Society},
    VOLUME = {24},
      YEAR = {1992},
    NUMBER = {4},
     PAGES = {325--334},
      ISSN = {0024-6093,1469-2120},
   MRCLASS = {17B37 (20G30)},
  MRNUMBER = {1165373},
MRREVIEWER = {H.\ H.\ Andersen},
       DOI = {10.1112/blms/24.4.325},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1112/blms/24.4.325},
}

@article{du1995canonical,
    AUTHOR = {Du, Jie},
     TITLE = {Canonical bases for irreducible representations of quantum
              {${\rm GL}_n$}. {II}},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {51},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {461--470},
      ISSN = {0024-6107,1469-7750},
   MRCLASS = {17B37 (20G05)},
  MRNUMBER = {1332884},
MRREVIEWER = {H.\ H.\ Andersen},
       DOI = {10.1112/jlms/51.3.461},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1112/jlms/51.3.461},
}


@article{skandera2008dual,
    AUTHOR = {Skandera, Mark},
     TITLE = {On the dual canonical and {K}azhdan-{L}usztig bases and 3412-,
              4231-avoiding permutations},
   JOURNAL = {J. Pure Appl. Algebra},
  FJOURNAL = {Journal of Pure and Applied Algebra},
    VOLUME = {212},
      YEAR = {2008},
    NUMBER = {5},
     PAGES = {1086--1104},
      ISSN = {0022-4049,1873-1376},
   MRCLASS = {05E05 (15A15 20C08)},
  MRNUMBER = {2387587},
MRREVIEWER = {Fabrizio\ Caselli},
       DOI = {10.1016/j.jpaa.2007.09.007},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1016/j.jpaa.2007.09.007},
}

@incollection{lusztig1994total,
  title={Total positivity in reductive groups},
  author={Lusztig, George},
  booktitle={Lie theory and geometry: in honor of Bertram Kostant},
  pages={531--568},
  year={1994},
  publisher={Springer}
}

@article{lusztig1997total,
  title={Total positivity and canonical bases},
  author={Lusztig, George},
  journal={Algebraic groups and Lie groups},
  volume={9},
  pages={281--295},
  year={1997}
}

@article {BB,
    AUTHOR = {Be\u{\i}linson, Alexandre and Bernstein, Joseph},
     TITLE = {Localisation de {$g$}-modules},
   JOURNAL = {C. R. Acad. Sci. Paris S\'{e}r. I Math.},
  FJOURNAL = {Comptes Rendus des S\'{e}ances de l'Acad\'{e}mie des Sciences.
              S\'{e}rie I. Math\'{e}matique},
    VOLUME = {292},
      YEAR = {1981},
    NUMBER = {1},
     PAGES = {15--18},
      ISSN = {0249-6291},
   MRCLASS = {14F05 (17B35 20G05)},
  MRNUMBER = {610137},
MRREVIEWER = {Floyd\ L.\ Williams},
}

@article{brylinski1981kazhdan,
    AUTHOR = {Brylinski, J.-L. and Kashiwara, M.},
     TITLE = {Kazhdan-{L}usztig conjecture and holonomic systems},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {64},
      YEAR = {1981},
    NUMBER = {3},
     PAGES = {387--410},
      ISSN = {0020-9910,1432-1297},
   MRCLASS = {22E47 (17B10 20G05)},
  MRNUMBER = {632980},
MRREVIEWER = {H.\ H.\ Andersen},
       DOI = {10.1007/BF01389272},
       URL = {https://doi-org.srv-proxy1.library.tamu.edu/10.1007/BF01389272},
}

@article{benderknuth1972,
title = {Enumeration of plane partitions},
journal = {Journal of Combinatorial Theory, Series A},
volume = {13},
number = {1},
pages = {40-54},
year = {1972},
issn = {0097-3165},
doi = {https://doi.org/10.1016/0097-3165(72)90007-6},
url = {https://www.sciencedirect.com/science/article/pii/0097316572900076},
author = {Edward A Bender and Donald E Knuth}
}

@article {CGP,
    AUTHOR = {Chmutov, Michael and Glick, Max and Pylyavskyy, Pavlo},
     TITLE = {The {B}erenstein-{K}irillov group and cactus groups},
   JOURNAL = {J. Comb. Algebra},
  FJOURNAL = {Journal of Combinatorial Algebra},
    VOLUME = {4},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {111--140},
      ISSN = {2415-6302},
   MRCLASS = {05E10},
  MRNUMBER = {4118639},
       DOI = {10.4171/JCA/36},
       URL = {https://doi-org.ezp1.lib.umn.edu/10.4171/JCA/36}
}


@article{SCHUTZENBERGER1972,
title = {Promotion des morphismes d'ensembles ordonn\'es},
journal = {Discrete Mathematics},
volume = {2},
number = {1},
pages = {73-94},
year = {1972},
issn = {0012-365X},
doi = {https://doi.org/10.1016/0012-365X(72)90062-3},
url = {https://www.sciencedirect.com/science/article/pii/0012365X72900623},
author = {M. P. Schützenberger}
}

@article {berenstein-kirilov,
    AUTHOR = {Berenstein, A. D. and Kirillov, A. N.},
     TITLE = {Groups generated by involutions, {G}elfand-{T}setlin
              patterns, and combinatorics of {Y}oung tableaux},
   JOURNAL = {Algebra i Analiz},
  FJOURNAL = {Rossi\u{\i}skaya Akademiya Nauk. Algebra i Analiz},
    VOLUME = {7},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {92--152},
      ISSN = {0234-0852},
   MRCLASS = {05E10 (05E15 20C30)},
  MRNUMBER = {1334154},
MRREVIEWER = {Alexander Postnikov},
}

@article {berenstein-zelevenski,
    AUTHOR = {Berenshte\u{\i}n, A. D. and Zelevinski\u{\i}, A. V.},
     TITLE = {When is the multiplicity of a weight equal to {$1$}?},
   JOURNAL = {Funktsional. Anal. i Prilozhen.},
  FJOURNAL = {Akademiya Nauk SSSR. Funktsional\cprime ny\u{\i} Analiz i ego
              Prilozheniya},
    VOLUME = {24},
      YEAR = {1990},
    NUMBER = {4},
     PAGES = {1--13, 96},
      ISSN = {0374-1990},
   MRCLASS = {17B10 (17B20)},
  MRNUMBER = {1092798},
MRREVIEWER = {Sen Qiu},
       DOI = {10.1007/BF01077330},
       URL = {https://doi.org/10.1007/BF01077330},
}


@article{chiang2024bender,
  title={Bender--{K}nuth involutions on linear extensions of posets},
  author={Chiang, Judy Hsin-Hui and Hoang, Anh Trong Nam and Kendall, Matthew and Lynch, Ryan and Nguyen, Son and Przybocki, Benjamin and Xia, Janabel},
  journal={Discrete Mathematics},
  volume={347},
  number={9},
  pages={114068},
  year={2024},
  publisher={Elsevier}
}

@article{nguyen2023cactus,
  title={The Cactus Group Property for Ordinal Sums of Disjoint Unions of Chains},
  author={Nguyen, Son},
  journal={arXiv preprint arXiv:2308.07240},
  year={2023}
}

@book{fulton1997young,
  title={Young tableaux: with applications to representation theory and geometry},
  author={Fulton, William},
  number={35},
  year={1997},
  publisher={Cambridge University Press}
}

@book{stanley2023enumerative,
  title={Enumerative {C}ombinatorics: {V}olume 2},
  author={Stanley, Richard},
  year={2023},
  publisher={Cambridge University Press}
}