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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/2506.11837 |
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| _version_ | 1866914007999315968 |
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| author | Lee, Mitchell |
| author_facet | Lee, Mitchell |
| contents | Let $r \geq 0$, and let $λ$ and $μ$ be partitions such that $λ_1 \leq r + 1$. We present a combinatorial interpretation of the plethysm coefficient $\langle s_λ, s_μ[s_r] \rangle$. As a consequence, we solve the restriction problem for partitions with at most three columns. That is, for all partitions $λ$ with $λ_1 \leq 3$, we find a combinatorial interpretation for the multiplicities of the irreducible $\mathfrak{S}_n$-submodules of the Schur module $\mathbb{S}^λ\mathbb{C}^n$, considered as an $\mathfrak{S}_n$-module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Restriction coefficients for partitions with at most three columns Lee, Mitchell Combinatorics Representation Theory 05E05 Let $r \geq 0$, and let $λ$ and $μ$ be partitions such that $λ_1 \leq r + 1$. We present a combinatorial interpretation of the plethysm coefficient $\langle s_λ, s_μ[s_r] \rangle$. As a consequence, we solve the restriction problem for partitions with at most three columns. That is, for all partitions $λ$ with $λ_1 \leq 3$, we find a combinatorial interpretation for the multiplicities of the irreducible $\mathfrak{S}_n$-submodules of the Schur module $\mathbb{S}^λ\mathbb{C}^n$, considered as an $\mathfrak{S}_n$-module. |
| title | Restriction coefficients for partitions with at most three columns |
| topic | Combinatorics Representation Theory 05E05 |
| url | https://arxiv.org/abs/2506.11837 |