English

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 PP-semigroups. Within the framework of C\mathcal C-semigroups, we define a finite-state automaton associated to them. Moreover, this automaton determines whether a C\mathcal C-semigroup is a PP-semigroup, which represents a bridge between affine semigroups and Discrete Mathematics. Furthermore, some algorithms for computing all the PP-semigroups with a fixed Frobenius element, genus, or multiplicity are provided.

Keywords

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}
}