On some affine semigroups characterized by a finite-state automata
Commutative Algebra
2025-10-16 v1 Combinatorics
Abstract
This work introduces a new kind of affine semigroups called -semigroups. Within the framework of -semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a -semigroup is a -semigroup, which represents a bridge between affine semigroups and Discrete Mathematics. Furthermore, some algorithms for computing all the -semigroups with a fixed Frobenius element, genus, or multiplicity are provided.
Cite
@article{arxiv.2510.13612,
title = {On some affine semigroups characterized by a finite-state automata},
author = {J. I. Farrán and J. C. Rosales and R. Tapia-Ramos and A. Vigneron-Tenorio},
journal= {arXiv preprint arXiv:2510.13612},
year = {2025}
}