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arXiv · 2510.13612

On some affine semigroups characterized by a finite-state automata

J. I. Farrán·J. C. Rosales·R. Tapia-Ramos·A. Vigneron-Tenorio
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Abstract

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

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J. I. Farrán, J. C. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio. 2025-10-15. On some affine semigroups characterized by a finite-state automata. https://arxiv.org/abs/2510.13612

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