@incollection {Ariki,
    AUTHOR = {Ariki, S.},
     TITLE = {Robinson-{S}chensted correspondence and left cells},
 BOOKTITLE = {Combinatorial methods in representation theory ({K}yoto,
              1998)},
    SERIES = {Adv. Stud. Pure Math.},
    VOLUME = {28},
     PAGES = {1--20},
 PUBLISHER = {Kinokuniya, Tokyo},
      YEAR = {2000},
   MRCLASS = {20C08 (05E15 20C30)},
  MRNUMBER = {1855588},
MRREVIEWER = {Cheng\ Dong\ Chen},
       DOI = {10.2969/aspm/02810001},
}

@book {Brualdi,
    AUTHOR = {Brualdi, R. A.},
     TITLE = {Introductory combinatorics},
   EDITION = {Fifth},
 PUBLISHER = {Pearson Prentice Hall, Upper Saddle River, NJ},
      YEAR = {2010},
     PAGES = {xii+605},
      ISBN = {978-0-13-602040-0; 0-13-602040-2},
   MRCLASS = {05-01},
  MRNUMBER = {2655770},
MRREVIEWER = {Jonathan\ Cutler},
}

@book {Bruns,
    AUTHOR = {Bruns, W. and Conca, A. and Raicu, C. and
              Varbaro, M.},
     TITLE = {Determinants, {G}r\"obner bases and cohomology},
    SERIES = {Springer Monographs in Mathematics},
 PUBLISHER = {Springer, Cham},
      YEAR = {[2022] \copyright 2022},
     PAGES = {xiii+507},
      ISBN = {978-3-031-05479-2; 978-3-031-05480-8},
   MRCLASS = {13P10 (13C40)},
  MRNUMBER = {4627943},
       DOI = {10.1007/978-3-031-05480-8},
}

@article {Procesi,
    AUTHOR = {de Concini, C. and Procesi, C.},
     TITLE = {A characteristic free approach to invariant theory},
   JOURNAL = {Advances in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {21},
      YEAR = {1976},
    NUMBER = {3},
     PAGES = {330--354},
   MRCLASS = {15A72 (14L99)},
  MRNUMBER = {422314},
MRREVIEWER = {Vladimir\ L.\ Popov},
       DOI = {10.1016/S0001-8708(76)80003-5},
}

@incollection {Diaconis,
    AUTHOR = {Diaconis, P. and Gangolli, A.},
     TITLE = {Rectangular arrays with fixed margins},
 BOOKTITLE = {Discrete probability and algorithms ({M}inneapolis, {MN},
              1993)},
    SERIES = {IMA Vol. Math. Appl.},
    VOLUME = {72},
     PAGES = {15--41},
 PUBLISHER = {Springer, New York},
      YEAR = {1995},
   MRCLASS = {05A15 (05B15 05E05 20C30)},
  MRNUMBER = {1380519},
MRREVIEWER = {Sinai\ Robins},
       DOI = {10.1007/978-1-4612-0801-3\_3},
}

@article {Rota,
    AUTHOR = {Doubilet, P. and Rota, G.-C. and Stein, J.},
     TITLE = {On the foundations of combinatorial theory. {IX}.
              {C}ombinatorial methods in invariant theory},
   JOURNAL = {Studies in Appl. Math.},
  FJOURNAL = {Studies in Applied Mathematics},
    VOLUME = {53},
      YEAR = {1974},
     PAGES = {185--216},
   MRCLASS = {15A72 (14M15)},
  MRNUMBER = {498650},
       DOI = {10.1002/sapm1974533185},
}

@article {Dyer,
    AUTHOR = {Dyer, M. and Kannan, R. and Mount, J.},
     TITLE = {Sampling contingency tables},
   JOURNAL = {Random Structures Algorithms},
  FJOURNAL = {Random Structures \& Algorithms},
    VOLUME = {10},
      YEAR = {1997},
    NUMBER = {4},
     PAGES = {487--506},
   MRCLASS = {68Q25 (60J10 62H17 68R05)},
  MRNUMBER = {1608222},
       DOI = {10.1002/(SICI)1098-2418(199707)10:4<487::AID-RSA4>3.0.CO;2-Q},
}

@book {Fulton,
    AUTHOR = {Fulton, W.},
     TITLE = {Young tableaux},
    SERIES = {London Mathematical Society Student Texts},
    VOLUME = {35},
      NOTE = {With applications to representation theory and geometry},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1997},
     PAGES = {x+260},
      ISBN = {0-521-56144-2; 0-521-56724-6},
   MRCLASS = {05E10 (05E05 05E15 14M15 20G05)},
  MRNUMBER = {1464693},
MRREVIEWER = {Tadeusz\ J\'ozefiak},
}

@Misc{M2,
          author = {Grayson, Daniel R. and Stillman, Michael E.},
          title = {Macaulay2, a software system for research in algebraic geometry},
          url = {http://www2.macaulay2.com},
        }

@incollection {Howe,
    AUTHOR = {Howe, R.},
     TITLE = {Perspectives on invariant theory: {S}chur duality,
              multiplicity-free actions and beyond},
 BOOKTITLE = {The {S}chur lectures (1992) ({T}el {A}viv)},
    SERIES = {Israel Math. Conf. Proc.},
    VOLUME = {8},
     PAGES = {1--182},
 PUBLISHER = {Bar-Ilan Univ., Ramat Gan},
      YEAR = {1995},
   MRCLASS = {13A50 (15A72 20G05 22E46)},
  MRNUMBER = {1321638},
MRREVIEWER = {Frank\ D.\ Grosshans},
}

@article {KL,
    AUTHOR = {Kazhdan, D. and Lusztig, G.},
     TITLE = {Representations of {C}oxeter groups and {H}ecke algebras},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {53},
      YEAR = {1979},
    NUMBER = {2},
     PAGES = {165--184},
   MRCLASS = {20H15 (17B35 20G05 22E47)},
  MRNUMBER = {560412},
MRREVIEWER = {Vinay\ V.\ Deodhar},
       DOI = {10.1007/BF01390031},
}

@incollection {Ram,
    AUTHOR = {Ram, A.},
     TITLE = {An elementary proof of {R}oichman's rule for irreducible
              characters of {I}wahori-{H}ecke algebras of type {A}},
 BOOKTITLE = {Mathematical essays in honor of {G}ian-{C}arlo {R}ota
              ({C}ambridge, {MA}, 1996)},
    SERIES = {Progr. Math.},
    VOLUME = {161},
     PAGES = {335--342},
 PUBLISHER = {Birkh\"auser Boston, Boston, MA},
      YEAR = {1998},
   MRCLASS = {05E10 (05E05 20C30)},
  MRNUMBER = {1627307},
MRREVIEWER = {Chanyoung\ Lee Shader},
}

@book {Serre,
    AUTHOR = {Serre, J.-P.},
     TITLE = {Linear representations of finite groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {Vol. 42},
   EDITION = {French},
 PUBLISHER = {Springer-Verlag, New York-Heidelberg},
      YEAR = {1977},
     PAGES = {x+170},
   MRCLASS = {20CXX},
  MRNUMBER = {450380},
MRREVIEWER = {W.\ Feit},
}

@article {Sidorov,
    AUTHOR = {Sidorov, S. V.},
     TITLE = {On the similarity of matrices with an integer spectrum over
              the ring of integers},
   JOURNAL = {Izv. Vyssh. Uchebn. Zaved. Mat.},
  FJOURNAL = {Izvestiya Vysshikh Uchebnykh Zavedeni\u i. Matematika.
              Kazanski\u i\ Gosudarstvenny\u i\ Universitet},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {86--94},
   MRCLASS = {15A21 (15B36)},
  MRNUMBER = {2919810},
MRREVIEWER = {V.\ V.\ Serge\u ichuk},
       DOI = {10.3103/S1066369X11030091},
}

@book {ECII,
    AUTHOR = {Stanley, R. P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {62},
      NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey
              Fomin},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1999},
     PAGES = {xii+581},
      ISBN = {0-521-56069-1; 0-521-78987-7},
   MRCLASS = {05A15 (05-02 05E05 05E10 68R05)},
  MRNUMBER = {1676282},
MRREVIEWER = {Ira\ Gessel},
       DOI = {10.1017/CBO9780511609589},
}

@misc{SY,
      AUTHOR = {Stelzer, A. and Yong, A.},
      EPRINT = {2410.23009},
  EPRINTTYPE = {arxiv},
       TITLE = {{RSK} as a linear operator},
        YEAR = {2024}}

@manual{sagemath,
    label        = {Sag95},
    author       = {{The Sage Developers}},
    title        = {{S}age{M}ath, the {S}age {M}athematics {S}oftware {S}ystem},
    url          = {https://www.sagemath.org},
    version      = {9.5},
    year         = {2022},
}