The catenary degree of the saturated numerical semigroups with prime multiplicity

TL;DR

This paper characterizes the catenary degree of saturated numerical semigroups with prime multiplicity, providing insights into their factorization structure and distances between factorizations.

Contribution

It introduces the set of saturated numerical semigroups with prime multiplicity and characterizes their catenary degree, a novel analysis in this context.

Findings

Characterization of the catenary degree for these semigroups

Identification of the set of saturated numerical semigroups with prime multiplicity

Insights into the factorization distances within these semigroups

Abstract

In this paper we present the set of saturated numerical semigroups with prime multiplicity. We also characterize the catenary degree of these semigroups that we acquire. The catenary degree of a numerical semigroup is the variant which measures the distance between factorizations of elements within that numerical semigroup.