Arf good semigroups with fixed conductor

TL;DR

This paper introduces a novel algorithm for computing Arf numerical semigroups with a fixed conductor and extends this to Arf good semigroups in higher dimensions, providing procedures for their enumeration.

Contribution

It presents a new algorithm for Arf semigroups with fixed conductor and extends the methodology to Arf good semigroups in multiple dimensions.

Findings

Algorithm efficiently computes Arf numerical semigroups with fixed conductor.

Procedures for enumerating Arf good semigroups in $ extbf{N}^r$ are developed.

Extension of the problem to higher-dimensional semigroups is achieved.

Abstract

In this paper we present a new algorithm to calculate the set of Arf numerical semigroups with given conductor. Moreover, we extend the previous problem to the class of good semigroups, presenting procedures to compute the set of the Arf good semigroups of $\mathbb{N}^r$ with a fixed conductor $\textbf{c} \in \mathbb{N}^r$, for all $r \in \mathbb{N}$.