Numerical semigroups from rational matrices I: power-integral matrices and nilpotent representations

2024/07/04 by Arsh Chhabra, Stephan Ramon Garcia, Chhabra, Arsh +5 · 2 citations
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Matrix Theory and Algorithms #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2407.03560

openalex publication_date 2024/07/04 · openalex created_date 2024/07/09 · openalex updated_date 2026/07/28

Abstract

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 matrix. We also obtain lower bounds on the size of such matrices and discuss the related class of power-integral matrices.

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• Numerical semigroups from rational matrices IV: computation of the matricial dimensions of numerical semigroups with small Frobenius number or genus
• Numerical semigroups from rational matrices III: semigroups of matricial dimension two and a counterexample to the lonely element conjecture

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