Semigroups with fixed multiplicity and embedding dimension

J. I. García-García; D. Marín-Aragón; M. A. Moreno-Frías; J. C. Rosales; A. Vigneron-Tenorio

paper

Semigroups with fixed multiplicity and embedding dimension

arXiv:1710.03523

Abstract

Given $m \in N,$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in ${m, m + 1, \dots, 2 m - 1} .$ In this work, packed numerical semigroups are used to built the set of numerical semigroups with fixed multiplicity and embedding dimension, and to create a partition in this set. Moreover, Wilf's conjecture is checked in the tree associated to some packed numerical semigroups.