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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| 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.