Abstract:We introduce a new decomposition of Young diagrams into thick hooks. These thick hook decompositions enable having a better control over hook products for excited diagrams in the Naruse hook length formula, which leads to improved bounds on the number of standard tableaux of skew shapes. 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 $n$. Finally, we recover some bounds of Pak and Panova on Kronecker coefficients with very short proofs that rely on characters.
From: Lucas Teyssier [view email]
[v1]
Sat, 9 Aug 2025 01:43:48 UTC (22 KB)
[v2]
Wed, 16 Sep 2026 23:18:40 UTC (53 KB)
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