On the computation of the Omega invariant of a numerical semigroup by optimizing over an efficient integer set

TL;DR

This paper introduces a new mathematical approach to compute the omega invariant of a numerical semigroup by formulating it as an optimization problem over an efficient set in a multiobjective linear integer program, supported by computational experiments.

Contribution

It presents a novel formulation and methodology for calculating the omega invariant using optimization over efficient sets in multiobjective integer programming.

Findings

The proposed algorithm effectively computes the omega invariant.

Computational experiments demonstrate the method's applicability.

The approach offers a new perspective for analyzing numerical semigroups.

Abstract

In this paper we present a mathematical formulation for the omega invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a multiobjective linear integer program. We offer a methodology to solve this problem and we provide some computational experiments to show the applicability of the proposed algorithm.