Numerical semigroups from rational matrices I: power-integral matrices and nilpotent representations
Arsh Chhabra, Stephan Ramon Garcia, Fangqian Zhang, Hechun Zhang
TL;DR
This paper introduces the concept of exponent semigroups for rational matrices, proving every numerical semigroup can be realized as such and exploring related classes like power-integral matrices.
Contribution
It establishes that all numerical semigroups can be represented as exponent semigroups of rational matrices and provides bounds on matrix sizes.
Findings
Every numerical semigroup is an exponent semigroup of some rational matrix.
Lower bounds on the size of matrices representing given semigroups.
Discussion of power-integral matrices related to exponent semigroups.
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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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Matrix Theory and Algorithms