5 papers · 1 filter
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…
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 of matricial dimension and produce a counterexample to the conjecture that a numerical semigroup whose small elements are lonel…
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…
Numerical semigroups from rational matrices II: matricial dimension does not exceed multiplicity
Arsh Chhabra, Stephan Ramon Garcia, Christopher O'Neill
We continue our study of exponent semigroups of rational matrices. Our main result is that the matricial dimension of a numerical semigroup is at most its multiplicity (the least g…
Numerical semigroups from rational matrices I: power-integral matrices and nilpotent representations
Arsh Chhabra, Stephan Ramon Garcia, Fangqian Zhang +1
Our aim in this paper is to initiate the study of exponent semigroups for rational matrices. We prove that every numerical semigroup is the exponent semigroup of some rational matr…