Nearly Gorenstein numerical semigroups with five generators have bounded type

TL;DR

This paper proves that nearly Gorenstein numerical semigroups generated by five integers have a bounded type, with a maximum of 40 for non-almost symmetric cases, and discusses implications for higher dimensions.

Contribution

It establishes a uniform bound on the type of nearly Gorenstein numerical semigroups with five generators, advancing understanding of their algebraic structure.

Findings

Type of such semigroups is at most 40 if not almost symmetric

Boundedness of type is proven for five-generator cases

Preliminary considerations for higher embedding dimensions

Abstract

We prove that the type of nearly Gorenstein numerical semigroups minimally generated by $5$ integers is bounded. In particular, if such a semigroup is not almost symmetric, then its type is at most $40$. Finally, we make some considerations in higher embedding dimension.