Related papers: Modular Frobenius pseudo-varieties

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…

This paper examines in a new way some known facts about numerical semigroups especially when the number of minimal generators (that is the embedding dimension) is at most three and at least two minimal generators are coprime. For such…

We define a reflective numerical semigroup of genus $g$ as a numerical semigroup that has a certain reflective symmetry when viewed within $\mathbb{Z}$ as an array with $g$ columns. Equivalently, a reflective numerical semigroup has one gap…

Let $a,b$ be positive integers. In this note, we study the numerical semigroup $H=\left<a,a+1,b\right>$ and and the associated numerical semigroup ring $R=k[[H]]$. Under the certain conditions, we provide explicit formulas for the Frobenius…

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…

Given the integers $0<r_1<\dots<r_k$, we consider the shifted family of semigroups $M_n=\langle n, n+r_1,\dots, n+r_k\rangle$, where $n>0$. For sufficiently large $n$, we prove that if $M_n$ is nearly Gorenstein or almost symmetric, then so…

We study integral almost square-free modular categories; i.e., integral modular categories of Frobenius-Perron dimension $p^nm$, where $p$ is a prime number, $m$ is a square-free natural number and ${\rm gcd}(p,m)=1$. We prove that if…

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.

A semigroup $S$ is called a weakly exponential semigroup if, for every couple $(a,b)\in S\times S$ and every positive integer $n$, there is a non-negative integer $m$ such that $(ab)^{n+m}=a^nb^n(ab)^m=(ab)^ma^nb^n$. A semigroup $S$ is…

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…

Let consider $n$ natural numbers $a\_1 ,\ldots , a\_{n} $. Let $S$ be the numerical semigroup generated by $a\_1 ,\ldots , a\_{n} $. Set $A=K[t^{a\_1}, \ldots , t^{a\_n}]=K[{x\_1}, \ldots , {x\_n}]/I$. The aim of this paper is:…

Let $A=(a_1, a_2, ..., a_n)$ be relative prime positive integers with $a_i\geq 2$. The Frobenius number $F(A)$ is the largest integer not belonging to the numerical semigroup $\langle A\rangle$ generated by $A$. The genus $g(A)$ is the…

In this paper, we study natural numbers $m$ with ${u_{z \pm 1} \equiv -1 \ (m)}$ for a $z \in \mathbb{N}$, where $u_n$ is the $n$th Fibonacci number. Furthermore, we want to show for $m \in \mathbb{N}\setminus\{0,1\}$: $[\forall p \…

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…

Numerical semigroups are cofinite additive submonoids of the natural numbers. In 2011, Keith and Nath illustrated an injection from numerical semigroups to integer partitions. We explore this connection between partitions and numerical…

We consider the complexity of deciding membership of a given finite semigroup to a fixed pseudovariety. While it is known that there exist pseudovarieties with NP-complete or even undecidable membership problems, for many well-known…

With any non necessarily orientable unpunctured marked surface (S,M) we associate a commutative algebra, called quasi-cluster algebra, equipped with a distinguished set of generators, called quasi-cluster variables, in bijection with the…

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…

Arithmetic quotients are quotients of bounded symmetric domains by arithmetic groups, and modular subvarieties of arithmetic quotients are themselves arithmetic quotients of lower dimension which live on arithmetic quotients, by an…

Let $\mathcal M_{mn}=\mathcal M_{mn}(\mathbb F)$ denote the set of all $m\times n$ matrices over a field $\mathbb F$, and fix some $n\times m$ matrix $A\in\mathcal M_{nm}$. An associative operation $\star$ may be defined on $\mathcal…