Anumerical semigroup is a subset ofN containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes...

We consider those positive integers that are not representable as linear combinations of terms of a generalized arithmetic progression with nonnegative integer coefficients. To do this, we make use of the numerical semigroup generated by a generalized arithmetic progression. The number of integers nonrepresentable by such a numerical semigroup is determined as well as that of its dual. In addit...

In this paper, we characterize those numerical semigroups containing 〈n1, n2〉. From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators.

In this article, we give a unified theory for constructing boundary layer expansions for discretized transport equations with homogeneous Dirichlet boundary conditions. We exhibit a natural assumption on the discretization under which the numerical solution can be written approximately as a two-scale boundary layer expansion. In particular, this expansion yields discrete semigroup estimates tha...

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers belonging to the semigroup. In a first approach, only homogeneous patterns where analized. In this contribution we study conditions for an eventually non-homoge...

We study numerical semigroups generated by intervals and solve the following problems related to such semigroups: the membership problem, give an explicit formula for the Frobe-nius number, decide whether the semigroup is a complete intersection and/or symmetric, and computation of the cardi-nality of a (any) minimal presentation of this kind of numerical semigroups. A numerical semigroup is a ...

Let S and Δ be numerical semigroups. A semigroup is an I(Δ)-semigroup if \ {0} ideal of Δ. We denote by ℐ (Δ) = {S | I(Δ)-semigroup}, we say that extension ∈ (Δ). In this work, present algorithm to build all the extensions a nu-merical semigroup. recursively ℐ0(ℕ) ℕ, ℐ1(ℕ) ℐ(ℕ) ℐk+1(ℕ) ℐ(ℐ k(ℕ)) for k ℕ. The complexity minimum set {k ℕ ℐk(ℕ)}. addition, introduce compute semigroups with fixed m...

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical ring flat algebra. In this paper, we show arithmetic and set-theoretic an equi-gcd