Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915437138149376 |
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| author | Teyssier, Lucas |
| author_facet | Teyssier, Lucas |
| contents | We bound the number of standard tableaux of skew shapes via thick hook decompositions in the Naruse hook length formula. Combining this with elementary counting arguments in the Murnaghan--Nakayama rule, we establish a uniform bound on characters of symmetric groups $\mathfrak{S}_n$. In the case of balanced representations, this improves on the character bounds of Féray and Śniady for permutations with support size at least $n^{2/3}$, and is sharp for permutations with support size of order $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06770 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions Teyssier, Lucas Combinatorics Representation Theory 05E10 (Primary) 20C30 (Secondary) We bound the number of standard tableaux of skew shapes via thick hook decompositions in the Naruse hook length formula. Combining this with elementary counting arguments in the Murnaghan--Nakayama rule, we establish a uniform bound on characters of symmetric groups $\mathfrak{S}_n$. In the case of balanced representations, this improves on the character bounds of Féray and Śniady for permutations with support size at least $n^{2/3}$, and is sharp for permutations with support size of order $n$. |
| title | Bounds on skew dimensions and characters of symmetric groups via thick hook decompositions |
| topic | Combinatorics Representation Theory 05E10 (Primary) 20C30 (Secondary) |
| url | https://arxiv.org/abs/2508.06770 |