On Row-Factorization relations of certain numerical semigroups

TL;DR

This paper studies the structure of numerical semigroups generated by almost arithmetic sequences, providing descriptions of row-factorization matrices for pseudo-Frobenius elements and characterizing their defining ideals in certain cases.

Contribution

It offers a detailed description of row-factorization matrices for pseudo-Frobenius elements and proves minimal generation of defining ideals for symmetric semigroups with embedding dimension 4 or 5.

Findings

Description of row-factorization matrices for pseudo-Frobenius elements

Minimal generating sets for defining ideals in specific symmetric cases

Characterization of relations in numerical semigroups generated by almost arithmetic sequences

Abstract

Let $H$ be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a description of a possible row-factorization $(\RF)$ matrix for each pseudo-Frobenius element of $H.$ Further, when $H$ is symmetric and has embedding dimension 4 or 5, we prove that the defining ideal is minimally generated by $\RF$-relations.