Related papers: Counting numerical semigroups
In this work we introduce the notion of almost-symmetry for generalized numerical semigroups. In addition to the main properties occurring in this new class, we present several characterizations for its elements. In particular we show that…
We provide a new way to represent numerical semigroups by showing that the position of every Ap\'ery set of a numerical semigroup $S$ in the enumeration of the elements of $S$ is unique, and that $S$ can be re-constructed from this…
In this paper we present a new approach to construct the set of numerical semigroups with a fixed genus. Our methodology is based on the construction of the set of numerical semigroups with fixed Frobenius number and genus. An equivalence…
A new general formula for the number of conjugacy classes of subgroups of given index in a finitely generated group is obtained.
A natural operation on numerical semigroups is taking a quotient by a positive integer. If $\mathcal S$ is a quotient of a numerical semigroup with $k$ generators, we call $\mathcal S$ a $k$-quotient. We give a necessary condition for a…
For any numerical semigroup $S$, there are infinitely many numerical symmetric semigroups $T$ such that $S=\frac{T}{2}$ is their half. We are studying the Betti numbers of the numerical semigroup ring $K[T]$ when $S$ is a 3-generated…
We characterize numerical semigroups for which the poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to union, intersection, infimum and supremum.
We find a relation between the genus of a quotient of a numerical semigroup $S$ and the genus of $S$ itself. We use this identity to compute the genus of a quotient of $S$ when $S$ has embedding dimension $2$. We also exhibit identities…
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…
Every numerical semigroup can be expressed as an intersection of irreducible numerical semigroups. We show that the unions of sets of lengths of factorizations of numerical semigroups into irreducible numerical semigroups are all equal to…
We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…
We introduce a module-theoretic approach and a linear-programming method to compute the matricial dimension of numerical semigroups. We use these to compute the matricial dimension of every numerical semigroup with Frobenius number at most…
The use of compositions simplifies some aspects of the theory of numerical semigroups. We illustrate this by giving a new proof for the asymptotic number C((1 + $\sqrt$ 5)/2) g of numerical semigroups of genus g and by describing the…
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…
A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…
Motivated by appearance of multisemigroups in the study of additive $2$-categories, we define and investigate the notion of a multisemigroup with multiplicities. This notion seems to be better suitable for applications in higher…
A \emph{numerical semigroup} is a subset $\Lambda$ of the nonnegative integers that is closed under addition, contains $0$, and omits only finitely many nonnegative integers (called the \emph{gaps} of $\Lambda$). The collection of all…
The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are…
We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…
In this paper we collect and improve the techniques for calculating the nuclei of a semifield and we use these tools to determine the order of the nuclei and of the center of some commutative presemifields of odd characteristic recently…