Related papers: Arf good semigroups
In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the root…
Let $S$ be an algebraic semigroup (not necessarily linear) defined over a field $F$. We show that there exists a positive integer $n$ such that $x^n$ belongs to a subgroup of $S(F)$ for any $x \in S(F)$. In particular, the semigroup $S(F)$…
The class of good semigroups is a class of subsemigroups of $N^h$, that includes the value semigroups of rings associated to curve singularities and their blowups, and allows to study combinatorically the properties of these rings. In this…
This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…
Let n_g denote the number of numerical semigroups of genus g. Bras-Amoros conjectured that n_g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree.…
We improve the previously best known lower and upper bounds on the number n_g of numerical semigroups of genus g. Starting from a known recursive description of the tree T of numerical semigroups, we analyze some of its properties and use…
An $\mathcal{A}$-semigroup is a numerical semigroup without consecutive small elements. This work generalizes this concept to finite-complement submonoids of an affine cone $\mathcal{C}$. We develop algorithmic procedures to compute all…
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…
We define the notion of a semicharacter of a group G : A function from the group to C*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is…
Good semigroups form a class of submonoids of $\mathbb{N}^d$ containing the value semigroups of curve singularities. In this article, we describe a partition of the complements of good semigroup ideals, having as main application the…
A numerical semigroup is a subset of N 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…
We study affine semigroup rings as algebras over subsemigroup rings. From this relative viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup algebras is constructed. Such a construction is compared to…
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.
In this paper we elaborate on the structure of the semigroup tree and the regularities on the number of descendants of each node observed earlier. These regularites admit two different types of behavior and in this work we investigate which…
A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number F, genus g and type t. It is known that for any numerical semigroup…
In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of…
We introduce the notion of numerical semigroups generated by concatenation of arithmetic sequences and show that this class of numerical semigroups exhibit multiple interesting behaviours.
A numerical semigroup is an additive submonoid of the natural numbers with finite complement. The size of the complement is called the genus of the semigroup. How many numerical semigroups have genus equal to $g$? We outline Zhai's proof of…
In this paper we describe an algorithm visiting all numerical semigroups up to a given genus using a well suited representation. The interest of this algorithm is that it fits particularly well the architecture of modern computers allowing…
We study how certain invariants of numerical semigroups relate to the number of second kind gaps. Furthermore, given two fixed non-negative integers F and k, we provide an algorithm to compute all the numerical semigroups whose Frobenius…