Affine semigroups and c-semigroups

Abstract

The presented PhD thesis is a compendium of three articles and has as its object of study affine semigroups and C-semigroups, from both a theoretical and computational perspective. Considering numerical semigroups as a starting point, the aim of this thesis is to generalize certain properties, characterizations, invariants, and known conjectures for the aforementioned structure, such as the Frobenius problem and Wilf's conjecture, to affine semigroups and C-semigroups. Furthermore, algorithms are presented to construct specific families of interest, such as B-semigroups and I(S)-semigroups, in order to partially address open problems or analyze certain properties of these families. Additionally, the quotient of any C-semigroup by a nonnegative integer is studied. As a consequence of the theoretical application of the proposed algorithms, examples are provided to illustrate the main results obtained.