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 …

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 …

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 …

A natural operation on numerical semigroups is taking a quotient by a positive integer. If, the
first known family of numerical semigroups that cannot be written as a k-quotient. We also …

We analyze the set of increasingly enumerable additive submonoids of R, for instance, the
set of logarithms of the positive integers with respect to a given base. We call them ω …

Let ng be the number of numerical semigroups of genus g. We present an approach to
compute ng by using even gaps, and the question: Is it true that n g+ 1> ng? is investigated …

A numerical semigroup S is an additive submonoid of NN whose complement is finite. The
cardinality of N _0 \ SN 0\S is called the genus of S and is denoted by g (S). The first nonzero …

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 …

We continue our study of exponent semigroups of rational matrices. Our main result is that
the matricial dimension of a numerical semigroup is at most its multiplicity (the least …

We study the atomic generalized numerical semigroups (GNSs), which naturally extend the
concept of atomic numerical semigroups. We introduce the notion of corner special gap and …