Numerical Semigroups with unique Apery expansions II

TL;DR

This paper investigates specific classes of numerical semigroups generated by arithmetic progression sums, focusing on their unique Apery set expansions and tangent cones in embedding dimension 5, providing a detailed algebraic analysis.

Contribution

It offers a comprehensive study of numerical semigroups with unique Apery expansions generated by arithmetic progressions in embedding dimension 5, expanding understanding of their algebraic properties.

Findings

Characterization of semigroups with unique Apery expansions

Analysis of tangent cones in embedding dimension 5

Identification of algebraic properties related to these classes

Abstract

In this paper, we carry out a fairly comprehensive study of special classes of numerical semigroups, and their tangent cones, generated by the sequence of partial sums of an arithmetic progression, in embedding dimension $5$. These classes have unique expansions of the Apery set elements.