**Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions.** / Paget, Rowena; Wildon, Mark.

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**Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions.** / Paget, Rowena; Wildon, Mark.

Research output: Contribution to journal › Article

Paget, R & Wildon, M 2019, 'Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions', *Proceedings of the London Mathematical Society*, vol. 118, no. 5, pp. 1153-1187. https://doi.org/10.1112/plms.12210

Paget, R., & Wildon, M. (2019). Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions. *Proceedings of the London Mathematical Society*, *118*(5), 1153-1187. https://doi.org/10.1112/plms.12210

Paget R, Wildon M. Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions. Proceedings of the London Mathematical Society. 2019 May;118(5):1153-1187. https://doi.org/10.1112/plms.12210

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title = "Generalized Foulkes modules and maximal and minimal constituents of plethysms of Schur functions",

abstract = "This paper proves a combinatorial rule giving all maximal and minimal partitions \lambda such that the Schur function s_\lambda appears in a plethysm of two arbitrary Schur functions. Determining the decomposition of these plethysmshas been identified by Stanley as a key open problem in algebraic combinatorics. As corollaries we prove three conjectures of Agaoka on the partitions labelling the lexicographically greatest and least Schur functions appearing in an arbitrary plethysm. We also show that the multiplicity of the Schur function labelled by the lexicographically least constituent may be arbitrarily large. The proof is carried out in the symmetric group and gives an explicit non-zero homomorphism corresponding to each maximal or minimal partition.",

author = "Rowena Paget and Mark Wildon",

year = "2019",

month = "5",

doi = "10.1112/plms.12210",

language = "English",

volume = "118",

pages = "1153--1187",

journal = "Proceedings of the London Mathematical Society",

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AU - Paget, Rowena

AU - Wildon, Mark

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N2 - This paper proves a combinatorial rule giving all maximal and minimal partitions \lambda such that the Schur function s_\lambda appears in a plethysm of two arbitrary Schur functions. Determining the decomposition of these plethysmshas been identified by Stanley as a key open problem in algebraic combinatorics. As corollaries we prove three conjectures of Agaoka on the partitions labelling the lexicographically greatest and least Schur functions appearing in an arbitrary plethysm. We also show that the multiplicity of the Schur function labelled by the lexicographically least constituent may be arbitrarily large. The proof is carried out in the symmetric group and gives an explicit non-zero homomorphism corresponding to each maximal or minimal partition.

AB - This paper proves a combinatorial rule giving all maximal and minimal partitions \lambda such that the Schur function s_\lambda appears in a plethysm of two arbitrary Schur functions. Determining the decomposition of these plethysmshas been identified by Stanley as a key open problem in algebraic combinatorics. As corollaries we prove three conjectures of Agaoka on the partitions labelling the lexicographically greatest and least Schur functions appearing in an arbitrary plethysm. We also show that the multiplicity of the Schur function labelled by the lexicographically least constituent may be arbitrarily large. The proof is carried out in the symmetric group and gives an explicit non-zero homomorphism corresponding to each maximal or minimal partition.

U2 - 10.1112/plms.12210

DO - 10.1112/plms.12210

M3 - Article

VL - 118

SP - 1153

EP - 1187

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 5

ER -