Theo Chinn | Searcharxiv

arXiv2026

Power-integral matrices over number fields: the Drazin inverse, pseudo-determinant, and numerical semigroups

We investigate matrices with entries in a number field such that some positive power has all its entries in the corresponding ring of integers. Our work generalizes previous results in several directions and we find applications to numerical semigroups.

math.NT↗

arXiv2025

Numerical semigroups from rational matrices IV: computation of the matricial dimensions of numerical semigroups with small Frobenius number or genus

We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimension of numerical semigroups. We use these to compute the matricial dimension of every numerical semigroup with Frobenius number at most $10$ or genus at most $6$. Many of these evaluations were beyond the scope of previous techniques.

math.CO↗