In 2013, Zhai proved that most numerical semigroups of a given genus have depth at most
$3 $ and that the number $ n_g $ of numerical semigroups of a genus $ g $ is asymptotic to …

We study the structure of the family of numerical semigroups with fixed multiplicity and
Frobenius number. We give an algorithmic method to compute all the semigroups in this …

Let S $\subseteq $ N be a numerical semigroup with multiplicity m= min (S\{0}) and
conductor c= max (N\S)+ 1. Let P be the set of primitive elements of S, and let L be the set of …

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 …

For a numerical semigroup, we encode the set of primitive elements that are larger than its
Frobenius number and show how to produce in a fast way the corresponding sets for its …

Let $\mathsf {r} _k $ be the unique positive root of $ x^ k-(x+ 1)^{k-1}= 0$. We prove the best
known bounds on the number $ n_ {g, d} $ of $ d $-dimensional generalized numerical …

A gapset is the complement of a numerical semigroup in ℕ\mathbb N. In this paper, we
characterize all gapsets of multiplicity m≤ 4. As a corollary, we provide a new simpler proof …

A gap a of a numerical semigroup S is fundamental if {2 a, 3 a}⊆ S. In this work, we will
study the set B (a)= S∣ S is a numerical semigroup and a is a fundamental gap of S. In …

Abstract Let S⊆ N be a numerical semigroup with multiplicity m= min (S∖{0}) and conductor
c= max (Z∖ S)+ 1. Let P be the set of primitive elements, ie minimal generators, of S, and let …

In this paper, we study gapsets and we focus on obtaining information on how the maximum
distance between two consecutive elements influences the behaviour of the set. In …