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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.21108 |
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| _version_ | 1866910895245885440 |
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| author | Lim, Ming Yean |
| author_facet | Lim, Ming Yean |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21108 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The number of irreducibles in the plethysm $s_λ[s_m]$ Lim, Ming Yean Combinatorics Representation Theory 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. |
| title | The number of irreducibles in the plethysm $s_λ[s_m]$ |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2503.21108 |