Related papers: Counting numerical semigroups
We describe the primitive central idempotents of the group algebra over a number field of finite monomial groups. We give also a description of the Wedderburn decomposition of the group algebra over a number field for finite strongly…
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…
We introduce square diagrams that represent numerical semigroups and we obtain an injection from the set of numerical semigroups into the set of Dyck paths.
Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…
We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the…
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…
Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and…
In this short note we count the finite semirings up to isomorphism, and up to isomorphism and anti-isomorphism for some small values of $n$; for which we utilise the existing library of small semigroups in the GAP package Smallsemi.
We study statistical properties of random numerical semigroups of a given genus. We analyze the graph of a typical numerical semigroup, understood as a function from $\mathbb{N}$ to $\mathbb{N}$. If $S$ is a numerical semigroup of genus…
A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are…
We built some congruences on semigroups, from where a decomposition of quasi-separative semigroups was obtained.
In this paper we study numerical semigroups of Sally type of multiplicity $e$ and embedding dimension $\nu \ge e-2$. We construct the minimal resolutions for these semigroup rings when they are symmetric and compute their Betti numbers. We…
We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.
Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements.…
A numerical semigroup is a subset of the non-negative integers that is closed under addition. For a randomly generated numerical semigroup, the expected number of minimum generators can be expressed in terms of a doubly-indexed sequence of…
In this short note we give a formula for the number of chains of subgroups of a finite elementary abelian $p$-group. This completes our previous work [5].
As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium--large (about a thousand digits) input data in a reasonably time cost on an ordinary computer.…
This paper is a continuation of the paper "Numerical Semigroups: Ap\'ery Sets and Hilbert Series". We consider the general numerical AA-semigroup, i.e., semigroups consisting of all non-negative integer linear combinations of relatively…
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
We present procedures to calculate the set of Arf numerical semigroups with given genus, given conductor and given genus and conductor. We characterize the Kunz coordinates of an Arf numerical semigroup. We also describe Arf numerical…