Related papers: Elasticity in Apery sets

In this paper we study numerical semigroups containing a given positive integer and closed with respect to the action of an affine map. For such semigroups we find a minimal set of generators, their embedding dimension, their genus and…

In this paper we initiate the study of $\aleph_0$-categorical semigroups, where a countable semigroup $S$ is $\aleph_0$-categorical if, for any natural number $n$, the action of its group of automorphisms Aut $S$ on $S^n$ has only finitely…

A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected components. We consider the problem of deciding whether two…

Let $\mathcal C \subset \mathbb N^p$ be a finitely generated integer cone and $S\subset \mathcal C$ be an affine semigroup such that the real cones generated by $\mathcal C$ and by $S$ are equal. The semigroup $S$ is called $\mathcal…

The delta set of a numerical semigroup $S$, denoted $\Delta(S)$, is a factorization invariant that measures the complexity of the sets of lengths of elements in $S$. We study the following problem: Which finite sets occur as the delta set…

Let a, k, h, c be positive integers and d a non zero integer. Recall that a numerical generalized almost arithmetic semigroup S is a semigroup minimally generated by relatively prime positive integers a, ha + d, ha + 2d, . . . , ha + kd, c,…

We study numerical semigroups with the property "multiplicity= embedding dimension+1", generated by concatenation of arithmetic sequences.

Given a set A of non-negative integers and a set B of positive integers,we are interested in computing all sets C (of positive integers) that are minimal in the family of sets K (of positive integers) such that (i) K contains no elements…

The equational probabilistic spectrum of a finite algebra is the set of probabilities with which equations are satisfied in the algebra. We study algebras with minimal spectrum, that is, spectra consisting only of the values $1$ and…

We associate a graph ${\mathcal N}_{S}$ with a semigroup $S$ (called the upper non-nilpotent graph of $S$). The vertices of this graph are the elements of $S$ and two vertices are adjacent if they generate a semigroup that is not nilpotent…

We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary…

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical semigroup algebra. In this paper, we show…

A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. The size of its complement is called the genus and the largest number in the complement is called its Frobenius number. We consider the set of…

Numerical semigroups with multiplicity $m$ are parameterized by integer points in a polyhedral cone $C_m$, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall…

Several recent papers have examined a rational polyhedron $P_m$ whose integer points are in bijection with the numerical semigroups (cofinite, additively closed subsets of the non-negative integers) containing $m$. A combinatorial…

Let $G$ be a subgroup of the symmetric group $S_n$. If the proportion of fixed-point-free elements in $G$ (or a coset) equals the proportion of fixed-point-free elements in $S_n$, then $G=S_n$. The analogue for $A_n$ holds if $n \ge 7$. We…

Let $M$ be a cancellative and commutative monoid. A non-invertible element of $M$ is called an atom (or irreducible element) if it cannot be factored into two non-invertible elements, while an atom $a$ of $M$ is called strong if $a^n$ has a…

A finite non-abelian group $H$ is hamiltonian if all of its subgroups are normal. We compute the minimal orders of graphs having a hamiltonian group as their automorphism group. The fixing number of a graph $\Gamma$ is the minimum…

Let $\mathcal S \subseteq \mathbb Z^m \oplus T$ be a finitely generated and reduced monoid. In this paper we develop a general strategy to study the set of elements in $\mathcal S$ having at least two factorizations of the same length,…

We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to…