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 …

We give an asymptotic estimate of the number of numerical semigroups of a given genus. In
particular, if ng is the number of numerical semigroups of genus g, we prove that g → ∞ n_g …

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 …

If S is a numerical semigroup, denote by g (S) the genus of S. A numerical semigroup T is an
I (S)-semigroup if T∖{0} is an ideal of S. If k∈ ℕ, then we denote by i (S, k) the number of I …

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 …

Let NN denote the monoid of natural numbers. A numerical semigroup is a cofinite
submonoid S ⊆ NS⊆ N. For the purposes of this paper, a generalized numerical semigroup …

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 …

Several recent papers have explored families of rational polyhedra whose integer points are
in bijection with certain families of numerical semigroups. One such family, first introduced …