Numerical semigroups from rational matrices II: matricial dimension does not exceed multiplicity

2024/07/22 by Chhabra, Arsh, Garcia, Stephan Ramon, O'Neill, Christopher · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.15571

Abstract

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 generator), greatly improving upon the previous upper bound (the conductor). For many numerical semigroups, including all symmetric numerical semigroups, our upper bound is tight.

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

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