Abstract: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.
| Subjects: | Combinatorics (math.CO) |
| Cite as: | arXiv:2605.25995 [math.CO] |
| (or arXiv:2605.25995v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25995 arXiv-issued DOI via DataCite (pending registration) |
From: Dor Elboim [view email]
[v1]
Mon, 25 May 2026 16:14:41 UTC (533 KB)
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