@article {AF,
    AUTHOR = {Adin, Ron M. and Frumkin, Avital},
     TITLE = {The conjugacy character of {$S_n$} tends to be regular},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {59},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {234--240},
   MRCLASS = {20C30},
  MRNUMBER = {920085},
MRREVIEWER = {G.\ D.\ James},
       DOI = {10.1007/BF02787264},
       URL = {https://doi.org/10.1007/BF02787264},
}

@misc {ART,
    AUTHOR = {Adin, Ron M. and Roichman, Yuval and Tsilevich, Natalia},
    EPRINT = {2509.12904},
    EPRINTTYPE = {arxiv},
    TITLE = {Asymptotics of higher Lie characters},
    YEAR = {2025}
}

@article {AS_Thrall,
    AUTHOR = {Ahlbach, Connor and Swanson, Joshua P.},
     TITLE = {Cyclic sieving, necklaces, and branching rules related to
              {T}hrall's problem},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {25},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {Paper No. 4.42, 38},
   MRCLASS = {05E15 (05E05 05E10)},
  MRNUMBER = {3891109},
       DOI = {10.37236/8198},
       URL = {https://doi.org/10.37236/8198},
}

@article {Almousa,
    AUTHOR = {Almousa, Ayah and Reiner, Victor and Sundaram, Sheila},
     TITLE = {Koszulity, supersolvability and {S}tirling representations},
   JOURNAL = {Ann. Represent. Theory},
  FJOURNAL = {Annals of Representation Theory},
    VOLUME = {2},
      YEAR = {2025},
    NUMBER = {2},
     PAGES = {173--247},
   MRCLASS = {16S37 (05B35)},
  MRNUMBER = {4917468},
       DOI = {10.5802/art.23},
       URL = {https://doi.org/10.5802/art.23},
}

@article {Armon,
    AUTHOR = {Armon, Sam and Swanson, Joshua P.},
     TITLE = {Super major index and {T}hrall's problem},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {8},
      YEAR = {2025},
    NUMBER = {3},
     PAGES = {795--815},
   MRCLASS = {17B10 (05E10 16W50 16W55 17B05)},
  MRNUMBER = {4925166},
       DOI = {10.5802/alco.421},
       URL = {https://doi.org/10.5802/alco.421},
}

@article {DesarmenienWachs,
    AUTHOR = {D\'esarm\'enien, Jacques and Wachs, Michelle L.},
     TITLE = {Descent classes of permutations with a given number of fixed points},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {64},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {311--328},
   MRCLASS = {05A15},
  MRNUMBER = {1245164},
MRREVIEWER = {Ira\ Gessel},
       DOI = {10.1016/0097-3165(93)90100-M},
       URL = {https://doi.org/10.1016/0097-3165(93)90100-M},
}

@article {DousseFeray,
    AUTHOR = {Dousse, Jehanne and F\'eray, Valentin},
     TITLE = {Asymptotics for skew standard {Y}oung tableaux via bounds for characters},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {147},
      YEAR = {2019},
    NUMBER = {10},
     PAGES = {4189--4203},
   MRCLASS = {05A16 (05E05 05E10 20C30)},
  MRNUMBER = {4002535},
MRREVIEWER = {Peter\ Vincent\ Hegarty},
       DOI = {10.1090/proc/14558},
       URL = {https://doi.org/10.1090/proc/14558},
}

@incollection {Garsia,
    AUTHOR = {Garsia, Adriano M.},
     TITLE = {Combinatorics of the free {L}ie algebra and the symmetric group},
 BOOKTITLE = {Analysis, et cetera},
     PAGES = {309--382},
 PUBLISHER = {Academic Press, Boston, MA},
      YEAR = {1990},
   MRCLASS = {17B01 (05A99 17B05 20C30)},
  MRNUMBER = {1039352},
MRREVIEWER = {Sen\ Qiu},
}

@article {GR93,
    AUTHOR = {Gessel, Ira M. and Reutenauer, Christophe},
     TITLE = {Counting permutations with given cycle structure and descent
              set},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {64},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {189--215},
   MRCLASS = {05A15 (05E05)},
  MRNUMBER = {1245159},
       DOI = {10.1016/0097-3165(93)90095-P},
       URL = {https://doi.org/10.1016/0097-3165(93)90095-P},
}

@article {GutierrezRosas,
    AUTHOR = {Guti\'errez, \'Alvaro and Rosas, Mercedes H.},
     TITLE = {Necessary conditions for the positivity of
              {L}ittlewood-{R}ichardson and plethystic coefficients},
   JOURNAL = {C. R. Math. Acad. Sci. Paris},
  FJOURNAL = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris},
    VOLUME = {361},
      YEAR = {2023},
     PAGES = {1163--1173},
   MRCLASS = {05E10},
  MRNUMBER = {4659076},
MRREVIEWER = {Allan\ Berele},
       DOI = {10.5802/crmath.468},
       URL = {https://doi.org/10.5802/crmath.468},
}

@article {Heide,
    AUTHOR = {Heide, Gerhard and Saxl, Jan and Tiep, Pham Huu and Zalesski,
              Alexandre E.},
     TITLE = {Conjugacy action, induced representations and the {S}teinberg
              square for simple groups of {L}ie type},
   JOURNAL = {Proc. Lond. Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {106},
      YEAR = {2013},
    NUMBER = {4},
     PAGES = {908--930},
   MRCLASS = {20D06 (20C33)},
  MRNUMBER = {3056296},
MRREVIEWER = {Hung\ Ngoc\ Nguyen},
       DOI = {10.1112/plms/pds062},
       URL = {https://doi.org/10.1112/plms/pds062},
}

@article {Hersh,
    AUTHOR = {Hersh, Patricia and Reiner, Victor},
     TITLE = {Representation stability for cohomology of configuration
              spaces in {$\Bbb R^d$}},
      NOTE = {With an appendix written jointly with Steven Sam},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2017},
    NUMBER = {5},
     PAGES = {1433--1486},
   MRCLASS = {20C15 (55R80)},
  MRNUMBER = {3658170},
MRREVIEWER = {Sadok\ Kallel},
       DOI = {10.1093/imrn/rnw060},
       URL = {https://doi.org/10.1093/imrn/rnw060},
}

@article {Inglis,
    AUTHOR = {Inglis, N. F. J. and Richardson, R. W. and Saxl, J.},
     TITLE = {An explicit model for the complex representations of {$S_n$}},
   JOURNAL = {Arch. Math. (Basel)},
  FJOURNAL = {Archiv der Mathematik},
    VOLUME = {54},
      YEAR = {1990},
    NUMBER = {3},
     PAGES = {258--259},
   MRCLASS = {20C30},
  MRNUMBER = {1037615},
MRREVIEWER = {Jorn\ B.\ Olsson},
       DOI = {10.1007/BF01188521},
       URL = {https://doi.org/10.1007/BF01188521},
}

@article {KraskiewiczWeyman,
    AUTHOR = {Kra\'skiewicz, Witold and Weyman, Jerzy},
     TITLE = {Algebra of coinvariants and the action of a {C}oxeter element},
   JOURNAL = {Bayreuth. Math. Schr.},
  FJOURNAL = {Bayreuther Mathematische Schriften},
    NUMBER = {63},
      YEAR = {2001},
     PAGES = {265--284},
   MRCLASS = {20C30 (05E10 17B01)},
  MRNUMBER = {1867283},
MRREVIEWER = {Christine\ Bessenrodt},
}

@article {Regev99,
    AUTHOR = {Regev, Amitai},
     TITLE = {Asymptotics of degrees of some {$S_n$}-sub regular
              representations},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {113},
      YEAR = {1999},
     PAGES = {15--28},
   MRCLASS = {05E10 (20C30)},
  MRNUMBER = {1729440},
MRREVIEWER = {Jennifer\ L.\ Morse},
       DOI = {10.1007/BF02780170},
       URL = {https://doi.org/10.1007/BF02780170},
}

@misc{Reiner-Banff,
    AUTHOR = {V. Reiner},
    TITLE = {Thrall's problem and coarsenings}, 
     NOTE =  {Banff workshop on positivity in algebraic combinatorics,  
    lecture slides},
    URL = {https://www-users.cse.umn.edu/~reiner/Talks/ThrallsProblem.pdf},
    YEAR = {2015}
}

@book {Reutenauer,
    AUTHOR = {Reutenauer, Christophe},
     TITLE = {Free {L}ie algebras},
    SERIES = {London Mathematical Society Monographs. New Series},
    VOLUME = {7},
      NOTE = {Oxford Science Publications},
 PUBLISHER = {The Clarendon Press, Oxford University Press, New York},
      YEAR = {1993},
     PAGES = {xviii+269},
   MRCLASS = {17-02 (05-02 17B05)},
  MRNUMBER = {1231799},
MRREVIEWER = {Hartmut\ Laue},
}

@article {R96,
    AUTHOR = {Roichman, Yuval},
     TITLE = {Upper bound on the characters of the symmetric groups},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {125},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {451--485},
   MRCLASS = {20C30},
  MRNUMBER = {1400314},
MRREVIEWER = {David\ Gluck},
       DOI = {10.1007/s002220050083},
       URL = {https://doi.org/10.1007/s002220050083},
}

@article {R97,
    AUTHOR = {Roichman, Yuval},
     TITLE = {Decomposition of the conjugacy representation of the symmetric
              groups},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {97},
      YEAR = {1997},
     PAGES = {305--316},
   MRCLASS = {20C30},
  MRNUMBER = {1441255},
MRREVIEWER = {G.\ D.\ James},
       DOI = {10.1007/BF02774043},
       URL = {https://doi.org/10.1007/BF02774043},
}

@article {Schocker,
    AUTHOR = {Schocker, Manfred},
     TITLE = {Multiplicities of higher {L}ie characters},
   JOURNAL = {J. Aust. Math. Soc.},
  FJOURNAL = {Journal of the Australian Mathematical Society},
    VOLUME = {75},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {9--21},
   MRCLASS = {20C30 (05E10)},
  MRNUMBER = {1984625},
MRREVIEWER = {Jonathan\ Brundan},
       DOI = {10.1017/S144678870000344X},
       URL = {https://doi.org/10.1017/S144678870000344X},
}

@article {Stanley1982,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Some aspects of groups acting on finite posets},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {32},
      YEAR = {1982},
    NUMBER = {2},
     PAGES = {132--161},
   MRCLASS = {06A10 (14L30 20B25)},
  MRNUMBER = {654618},
MRREVIEWER = {R.\ J.\ Bumcrot},
       DOI = {10.1016/0097-3165(82)90017-6},
       URL = {https://doi.org/10.1016/0097-3165(82)90017-6},
}

@book {Stanley_ECII,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {208},
   EDITION = {Second},
      NOTE = {With an appendix by Sergey Fomin},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {[2024] \copyright 2024},
     PAGES = {xvi+783},
       DOI = {10.1017/9781009262538},
       URL = {https://doi.org/10.1017/9781009262538},
}

@article {Sundaram18,
    AUTHOR = {Sundaram, Sheila},
     TITLE = {On conjugacy classes of {$S_n$} containing all irreducibles},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {225},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {321--342},
   MRCLASS = {05E10 (05E05)},
  MRNUMBER = {3805649},
MRREVIEWER = {Zhicong\ Lin},
       DOI = {10.1007/s11856-018-1659-3},
       URL = {https://doi.org/10.1007/s11856-018-1659-3},
}

@article {Swanson,
    AUTHOR = {Swanson, Joshua P.},
     TITLE = {On the existence of tableaux with given modular major index},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {1},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {3--21},
   MRCLASS = {05E10 (05A20)},
  MRNUMBER = {3857157},
MRREVIEWER = {Elizabeth\ M.\ Niese},
       DOI = {10.5802/alco.4},
       URL = {https://doi.org/10.5802/alco.4},
}

@article {Thrall,
    AUTHOR = {Thrall, R. M.},
     TITLE = {On symmetrized {K}ronecker powers and the structure of the
              free {L}ie ring},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {64},
      YEAR = {1942},
     PAGES = {371--388},
   MRCLASS = {09.1X},
  MRNUMBER = {6149},
MRREVIEWER = {R.\ Brauer},
       DOI = {10.2307/2371691},
       URL = {https://doi.org/10.2307/2371691},
}

@article {VershikKerovPlanch,
    AUTHOR = {Vershik, A. M. and Kerov, S. V.},
     TITLE = {Asymptotic behavior of the {P}lancherel measure of the
              symmetric group and the limit form of {Y}oung tableaux},
   JOURNAL = {Dokl. Akad. Nauk SSSR},
  FJOURNAL = {Doklady Akademii Nauk SSSR},
    VOLUME = {233},
      YEAR = {1977},
    NUMBER = {6},
     PAGES = {1024--1027},
   MRCLASS = {10J20 (20C30)},
  MRNUMBER = {480398},
MRREVIEWER = {V.\ M.\ Maksimov},
}