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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.25995 |
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| _version_ | 1866917532163637248 |
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| author | Aggarwal, Amol Elboim, Dor |
| author_facet | Aggarwal, Amol Elboim, Dor |
| contents | We prove that the maximal dimension $d_N$ of an irreducible representation of the symmetric group $S_N$ satisfies
$$d_N=\sqrt{N!} \, e^{-(\mathfrak{d}+o(1))\sqrt{N} }, \quad N\to \infty,$$
for some constant $\mathfrak{d}>0$. This answers a question raised by Vershik--Kerov in 1985. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25995 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the maximal dimension of an irreducible representation of the symmetric group Aggarwal, Amol Elboim, Dor Combinatorics We prove that the maximal dimension $d_N$ of an irreducible representation of the symmetric group $S_N$ satisfies $$d_N=\sqrt{N!} \, e^{-(\mathfrak{d}+o(1))\sqrt{N} }, \quad N\to \infty,$$ for some constant $\mathfrak{d}>0$. This answers a question raised by Vershik--Kerov in 1985. |
| title | On the maximal dimension of an irreducible representation of the symmetric group |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.25995 |