Delta sets for symmetric numerical semigroups with embedding dimension three

TL;DR

This paper extends the understanding of Delta sets to symmetric numerical semigroups with embedding dimension three, providing a fast algorithm and a complete characterization of possible Delta sets.

Contribution

It introduces a fast algorithm for computing Delta sets in symmetric embedding dimension three semigroups and characterizes all realizable Delta sets.

Findings

Fast algorithm for Delta set computation

Complete characterization of Delta sets

Extension of non-symmetric results to symmetric cases

Abstract

This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to compute the Delta set of any embedding dimension three numerical semigroup. Also, as a consequence of these resutls, the sets that can be realized as Delta sets of numerical semigroups of embedding dimension three are fully characterized.