Almost symmetric numerical semigroups with given Frobenius number and type

TL;DR

This paper introduces efficient algorithms to enumerate all almost symmetric numerical semigroups with a specified Frobenius number and type, enhancing computational methods in algebraic semigroup theory.

Contribution

The authors develop and implement two novel algorithms for computing all almost symmetric numerical semigroups with fixed Frobenius number and type, improving efficiency over existing methods.

Findings

Algorithms successfully enumerate semigroups with given parameters.

Implementation in GAP package NumericalSgps enhances computational tools.

Efficiency comparable or superior to previous algorithms.

Abstract

We give two algorithmic procedures to compute the whole set of almost symmetric numerical semigroups with fixed Frobenius number and type, and the whole set of almost symmetric numerical semigroups with fixed Frobenius number. Our algorithms allow to compute the whole set of almost symmetric numerical semigroups with fixed Frobenius number with similar or even higher efficiency that the known ones. They have been implemented in the GAP (http://www.gap-system.org) package NumericalSgps (http://www.gap-system.org/Packages/numericalsgps.html).