Kenny Lau

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math.CO2026

Zero-free columns in character tables of symmetric groups

Colin Defant, Sidharth Hariharan, Kenny Lau +1

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 $S_{n}$ …

math.CO2026

Dead ends in square-free digit walks

Evan Chen, Chris Cummins, Ben Eltschig +18

We study "dead ends" in square-free digit walks: square-free integers $N$ such that, in base $b$ , every one-digit extension $b N + d$ is non-square-free. In base $10$ , the stochastic…

math.CO2026

Fel's Conjecture on Syzygies of Numerical Semigroups

Evan Chen, Chris Cummins, GSM +18

Let $S = ⟨ d_{1}, \dots, d_{m} ⟩$ be a numerical semigroup and $k [S]$ its semigroup ring. The Hilbert numerator of $k [S]$ determines normalized alternating syzygy power sums $K_…