Supersymmetric gaps of a numerical semigroup with two generators

TL;DR

This paper introduces the concepts of supersymmetric and self-symmetric gaps in two-generator numerical semigroups, showing these gaps uniquely determine the semigroup and relate to fundamental gaps.

Contribution

It defines new symmetry-based gap concepts and proves they fully characterize two-generator numerical semigroups, linking to fundamental gaps.

Findings

Supersymmetric and self-symmetric gaps determine the semigroup.

These gaps relate to the semigroup's fundamental gaps.

The concepts provide new symmetry insights into semigroup structure.

Abstract

In this paper we introduce the new concepts of supersymmetric and self-symmetric gaps of a numerical semigroup with two generators. Those concepts are based on certain symmetries of the gaps of the semigroup with respect to their Wilf number. We prove that the set of supersymmetric and self-symmetric gaps completely determines the semigroup and we compare this set with the fundamental gaps of the semigroup.