Work

Numerical Semigroups From Rational Matrices Ii: Matricial Dimension Does Not Exceed Multiplicity

Year: 2024

Type: article

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. Our construction uses combinatorially structured matrices and is parametrised by Kunz coordinates, which are central to enumerative problems in the study of numerical semigroups.

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972724001035

Authors: ARSH CHHABRA, STEPHAN RAMON GARCIA, CHRISTOPHER O’NEILL

Institutions: Pomona College, San Diego State University

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

Funder: National Science Foundation