Let {a1, . . . , ap} be the minimal generating set of a numerical monoid S. For any s ∈ S, its Delta set is defined by ∆xiai and xi ∈ N for all i}. The Delta set of a numerical monoid S, denoted by ∆(S), is the union of all the sets ∆(s) with s ∈ S. As proved in [5], there exists a bound N such that ∆(S) is the union of the sets ∆(s) with s ∈ S and s < N . In this work, we obtain a sharpened bound and we present an algorithm for the computation of ∆(S) that requires only the factorizations of a1 elements.

Abstract. In this paper, we deal with the problem of the uniqueness of a minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for the uniqueness of such a minimal system of generators. These conditions come from the study and combinatorial description of the so-called indispensable binomials in the semigroup ideal.

Let C ⊂ Q p be a rational cone. An affine semigroup S ⊂ C is a C-semigroup whenever (C \ S) ∩ N p has only a finite number of elements.In this work, we study the tree of C-semigroups, give a method to generate it and study their subsemigroups with minimal embedding dimension. We extend Wilf's conjecture for numerical semigroups to Csemigroups and give some families of C-semigroups fulfilling the extended conjecture. We also check that other conjectures on numerical semigroups seem to be also satisfied by C-semigroups.

This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those algebras is related to the combinatorics of some simplicial complexes. Our description may be interpreted as an algorithmic procedure to partially compute this resolution.Comment: 20 pages, this work was presented as a poster at the 'International Conference on Commutative, Combinatorial and Computational Algebra in Honour of Pilar Pison Casares' Seville, February 11 - 16, 2008. http://departamento.us.es/da/actividades/ciaccc.ht

We give an algorithm to compute the ω-primality of finitely generated atomic monoids. Asymptotic ω-primality is also studied and a formula to obtain it in finitely generated quasi-Archimedean monoids is proven. The formulation is applied to numerical semigroups, obtaining an expression of this invariant in terms of its system of generators.