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Semigroups with fixed multiplicity and embedding dimension (1710.03523v1)
Published 10 Oct 2017 in math.AC and math.NT
Abstract: Given $m\in \mathbb{N},$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in ${m,m+1,\ldots, 2m-1}.$ 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.
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