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S. Hariharan

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Preprint Aug 2026

Zero-free columns in character tables of symmetric groups

The rows and columns of the character table of the symmetric group $S_n$ are both naturally indexed by partitions of $n$. Let $D(n)$ denote the number of conjugacy classes of $S_n$ whose column contains no zero entry. The identity column is always zero-free, so $D(n)\geq 1$. It is known that $D(n)\ll n^2$. We prove tha...

Colin Defant, S. Hariharan, Kenny Lau et al. · 0 citations