This book is an extended and revised version of" Numerical Semigroups with Applications,"
published by Springer as part of the RSME series. Like the first edition, it presents …

A numerical semigroup is an additive submonoid of the natural numbers with finite
complement. The size of the complement is called the genus of the semigroup. How many …

This paper intends to survey the vast literature devoted to a problem posed by Wilf in 1978
which, despite the attention it attracted, remains unsolved. As it frequently happens with …

Let S⊆ N be a numerical semigroup with multiplicity m= min (S\{0}), conductor c= max
(N\S)+ 1 and minimally generated by e elements. Let L be the set of elements of S which are …

For g≥ 0, let ng denote the number of numerical semigroups of genus g. A conjecture by
Maria Bras-Amorós in 2008 states that the inequality ng≥ ng− 1+ ng− 2 holds for all g≥ 2 …

Abstract Let C ⊂ Q^ p_+ C⊂ Q+ p be a rational cone. An affine semigroup S ⊂ CS⊂ C is a
C C-semigroup whenever (C ∖ S) ∩ N^ p (C\S)∩ N p has only a finite number of elements …

For a numerical semigroup S⊆ N, let m, e, c, g denote its multiplicity, embedding dimension,
conductor and genus, respectively. Wilf's conjecture (1978) states that e (c− g)≥ c. As of …

Abstract Let S ⊆\mathbb NS⊆ N be a numerical semigroup with multiplicity m, conductor c
and minimal generating set P. Let L= S ∩ 0, c-1 L= S∩ 0, c-1 and W (S)=| P|| L|-c W (S)=| P …

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 …

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 …