Comptes Rendus
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Combinatorics
Plethysm and a character embedding problem of Miller
Brendon Rhoades1 
1 Department of Mathematics, University of California, San Diego La Jolla, CA, 92093, USA
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1113-1116.

We use a plethystic formula of Littlewood to answer a question of Miller on embeddings of symmetric group characters. We also reprove a result of Miller on character congruences.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.363

Brendon Rhoades 1

1 Department of Mathematics, University of California, San Diego La Jolla, CA, 92093, USA
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Brendon Rhoades. Plethysm and a character embedding problem of Miller. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1113-1116. doi : 10.5802/crmath.363. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.363/

[1] Alain Lascoux; Bernard Lecrec; Jean-Yves Thibon Ribbon tableaux, Hall–Littlewood symmetric functions, quantum affine algebras, and unipotent varieties, J. Math. Phys., Volume 38 (1997) no. 2, pp. 1041-1068 | DOI | Zbl

[2] Dudley E. Littlewood Modular representations of symmetric groups, Proc. R. Soc. Lond., Ser. A, Volume 209 (1951), pp. 333-353 | MR | Zbl

[3] Ian G. Macdonald Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, Oxford University Press, 1995 | Zbl

[4] Alexander R. Miller Personal communication (2021)

[5] Alexander R. Miller Congruences in character tables of symmetric groups (2019) (https://arxiv.org/abs/1908.03741v1)

[6] Brendon Rhoades Hall–Littlewood polynomials and fixed point enumeration, Discrete Math., Volume 310 (2010) no. 4, pp. 869-876 | DOI | MR | Zbl

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