Related papers: Computing the number of numerical semigroups using…
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in…
Let $\mathbb{N}^{d}$ be the $d$-dimensional monoid of non-negative integers. A generalized numerical semigroup is a submonoid $ S\subseteq \mathbb{N}^d$ such that $H(S)=\mathbb{N}^d \setminus S$ is a finite set. We introduce irreducible…
A polynomial time algorithm to give a complete description of all subfields of a given number field was given in an article by van Hoeij et al. This article reports on a massive speedup of this algorithm. This is primary achieved by our new…
Numerical monoids (cofinite, additive submonoids of the non-negative integers) arise frequently in additive combinatorics, and have recently been studied in the context of factorization theory. Arithmetical numerical monoids, which are…
In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing the structure of a finite semigroup from a generating set. As was the case with the original algorithm of Froidure and Pin, the algorithms presented…
We present an algorithm to explore various properties of the numerical semigroups with a given maximum primitive. In particular, we count the number of such numerical semigroups and verify that there is no counterexample to Wilf's…
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…
This paper is concerned with the computation of representation matrices for the action of Frobenius to the cohomology groups of algebraic varieties. Specifically we shall give an algorithm to compute the matrices for arbitrary algebraic…
Let $n$ be a positive integer greater than $2$. We define \textit{the Proth numerical semigroup}, $P_{k}(n)$, generated by $\{k 2^{n+i}+1 \,\mid\, i \in \mathbb{N}\}$, where $k$ is an odd positive number and $k < 2^{n}$. In this paper, we…
In this paper we study the limit theory of numerical semigroups with two generators. We give a complete axiomatization in some cases.
Given a numerical semigroup $S$ and a positive integer $d$, the fraction $\frac{S}{d}=\{ x \in \mathbb{N} \ | \ dx \in S\}$ is again a numerical semigroup. In this paper we determine a generating set for $\frac{S}{d}$ in terms of the…
Using generating functions, we enumerate regular semisimple conjugacy classes in the finite classical groups. For the general linear, unitary, and symplectic groups this gives a different approach to known results; for the special…
The greatest integer that does not belong to $S$ is the Frobenius number of $S$ and denoted by $F(S)$. To solve the Frobenius problem means the study to find $F(S)$. The Frobenius problem have treated steadily for a long time. In this…
A numerical set is a co-finite subset of the natural numbers that contains zero. Its Frobenius number is the largest number in its complement. Each numerical set has an associated semigroup $A(T)=\{t\mid t+T\subseteq T\}$, which has the…
We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields…
A generalised numerical semigroup (GNS) is a submonoid $S$ of $\mathbb{N}^d$ for which the complement $\mathbb{N}^d\setminus S$ is finite. The points in the complement $\mathbb{N}^d\setminus S$ are called gaps. A gap $F$ is considered…
In this paper, we extend recent results about the distribution of even and odd gaps of a numerical semigroup. We find that, for any numerical semigroup, the distribution can be computed in terms of the numbers of or the sums of odd and even…
We study statistical properties of numerical semigroups of genus $g$ as $g$ goes to infinity. More specifically, we answer a question of Eliahou by showing that as $g$ goes to infinity, the proportion of numerical semigroups of genus $g$…
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we factorize these semigroups as products of semigroups that…
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…