Related papers: Genus of numerical semigroups generated by three e…

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…

For a nonnegative integer $p$, we give explicit formulas for the $p$-Frobenius number and the $p$-genus of generalized Fibonacci numerical semigroups. Here, the $p$-numerical semigroup $S_p$ is defined as the set of integers whose…

We examine two natural operations to create numerical semigroups. We say that a numerical semigroup $\mathcal{S}$ is $k$-normalescent if it is the projection of the set of integer points in a $k$-dimensional polyhedral cone, and we say that…

This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three…

We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.

Let $\Delta$ be a numerical semigroup and let $d\ge 2$ be an integer. We study the fiber of the quotient map \(S\mapsto S/d\) over $\Delta$. We describe its elements as semigroups of the form $\langle X\rangle+d\Delta$, for suitable finite…

Let 0 < a < b be two relatively prime integers and let <a,b> be the numerical semigroup generated by a and b with Frobenius number g(a,b)=ab-a-b. In this note, we prove that there exists a prime number p in <a,b> with p < g(a,b) when the…

This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams,…

A generalized numerical semigroup is a submonoid of $\mathbb{N}^d$ with finite complement in it. In this work we study some properties of three different classes of generalized numerical semigroups. In particular, we prove that the first…

We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval, a formula for the $r^{th}$ Feng-Rao number is obtained.

This paper shows how to construct explicitly an automaton that generates an arbitrary numerical semigroup.

A numerical semigroup is a submonoid of ${\mathbb Z}_{\ge 0}$ whose complement in ${\mathbb Z}_{\ge 0}$ is finite. For any set of positive integers $a,b,c$, the numerical semigroup $S(a,b,c)$ formed by the set of solutions of the inequality…

We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.

Ulrich ideals in numerical semigroup rings of small multiplicity are studied. If the semigroups are three-generated but not symmetric, the semigroup rings are Golod, since the Betti numbers of the residue class fields of the semigroup rings…

Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…

We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroups with embedding dimension three.

In this paper we introduce the concept of corner element of a generalized numerical semigroup, which extends in a sense the idea of conductor of a numerical semigroup to generalized numerical semigroups in higher dimensions. We present…

This paper presents an algorithm for generating pseudorandom numbers using quasigroups. Random numbers have several applications in the area of secure communication. The proposed algorithm uses a matrix of size n x n which is pre-generated…

A numerical semigroup is said to be universally free if it is free for any possible arrangement of its minimal generating set. In this work, we establish that toric ideals associated with universally free numerical semigroups can be…

In this paper we present the set of saturated numerical semigroups with prime multiplicity. We also characterize the catenary degree of these semigroups that we acquire. The catenary degree of a numerical semigroup is the variant which…