Which sets are sets of lengths in all numerical monoids ?

TL;DR

This paper characterizes the specific sets of nonnegative integers that appear as sets of lengths in every numerical monoid, providing a comprehensive understanding of their universal properties.

Contribution

It explicitly identifies the sets of lengths that are common to all numerical monoids, a novel characterization in the study of non-unique factorizations.

Findings

Identified the universal sets of lengths in all numerical monoids

Provided explicit criteria for these sets

Enhanced understanding of factorization invariants

Abstract

We explicitly determine those sets of nonnegative integers which occur as sets of lengths in all numerical monoids.