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Bibliographic Details
Main Author: Lim, Ming Yean
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.21108
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Table of Contents:
  • We give a formula for the number of irreducibles (with multiplicity) in the decomposition of the plethysm $s_λ[s_m]$ of Schur functions in terms of the number of lattice points in certain rational polytopes. In the case where $λ= n$ consists of a single part, we will give a combinatorial interpretation of this number as the cardinality of a set of matrices modulo permutation equivalence. This is also the setting of Foulkes' conjecture, and our results allow us to state a weaker version that only involves comparing the cardinalities of such sets, rather than the multiplicities of irreducible representations.