Characterizing affine C-semigroups

2019/07/07 by J. D. Díaz-Ramírez, J. I. García-García, Díaz-Ramírez, J. D. +5
Engineering · Computer Science · Decision Sciences · #Scheduling and Optimization Algorithms #semigroups and automata theory #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1907.03276

Abstract

Let \mathcal C ⊂ \mathbb N^p be a finitely generated integer cone and S⊂ \mathcal C be an affine semigroup such that the real cones generated by \mathcal C and by S are equal. The semigroup S is called \mathcal C-semigroup if \mathcal C∖ S is a finite set. In this paper, we characterize the \mathcal C-semigroups from their minimal generating sets, and we give an algorithm to check if S is a \mathcal C-semigroup and to compute its set of gaps. We also study the embedding dimension of \mathcal C-semigroups obtaining a lower bound for it, and introduce some families of \mathcal C-semigroups whose embedding dimension reaches our bound. In the last section, we present a method to obtain a decomposition of a \mathcal C-semigroup into irreducible \mathcal C-semigroups.

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