Stephan Ramon Garcia

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20242026

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3 papers · 1 filter

math.CO2025

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 +1

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…

math.CO2025

Numerical semigroups from rational matrices III: semigroups of matricial dimension two and a counterexample to the lonely element conjecture

Arsh Chhabra, Stephan Ramon Garcia

We characterize semigroups in ${0, 1, 2, \dots}$ of matricial dimension $2$ and produce a counterexample to the conjecture that a numerical semigroup whose small elements are lonel…

math.CO2025

Factorization length distribution for affine semigroups V: explicit asymptotic behavior of weighted factorization lengths on numerical semigroups

Stephan Ramon Garcia, Gabe Udell

We describe the asymptotic behavior of weighted factorization lengths on numerical semigroups. Our approach is geometric as opposed to analytic, explains the presence of Curry-Scho…