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arXiv · 2407.03560

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

Arsh Chhabra·Stephan Ramon Garcia·Fangqian Zhang·Hechun Zhang
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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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Arsh Chhabra, Stephan Ramon Garcia, Fangqian Zhang, Hechun Zhang. 2024-09-02. Numerical semigroups from rational matrices I: power-integral matrices and nilpotent representations. https://arxiv.org/abs/2407.03560

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