no. G10
Combinatoire
Plethysm and a character embedding problem of Miller
Rhoades, Brendon1 
1 Department of Mathematics, University of California, San Diego La Jolla, CA, 92093, USA
Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, 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.

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Révisé le :
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DOI : 10.5802/crmath.363
Rhoades, Brendon 1

1 Department of Mathematics, University of California, San Diego La Jolla, CA, 92093, USA 
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Rhoades, Brendon. Plethysm and a character embedding problem of Miller. Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1113-1116. doi : 10.5802/crmath.363. http://www.numdam.org/articles/10.5802/crmath.363/

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

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

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

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

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

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