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arXiv · 2510.15209

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

Theo Chinn·Junshu Feng·Stephan Ramon Garcia·Peiting Jiang
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Abstract

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.

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Theo Chinn, Junshu Feng, Stephan Ramon Garcia, Peiting Jiang. 2025-10-17. Numerical semigroups from rational matrices IV: computation of the matricial dimensions of numerical semigroups with small Frobenius number or genus. https://arxiv.org/abs/2510.15209

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