Some Families of Greedy Numerical Semigroups

TL;DR

This paper explores new families of greedy numerical semigroups, which are special types of numerical semigroups where greedy representations are optimal, extending the concept from the change-making problem.

Contribution

It identifies and characterizes new families of greedy numerical semigroups, expanding understanding of their structure and properties.

Findings

New families of greedy numerical semigroups identified

Characterization of these families provided

Extension of the change-making problem to broader semigroup classes

Abstract

The change-making problem was recently extended to sets of positive integers not containing the element $1$, and from there to numerical semigroups. A greedy numerical semigroup is defined as a numerical semigroup where the greedy representation of an element is optimal with respect to the number of summands. In this paper we identify some new families of greedy numerical semigroups.