The tree of irreducible numerical semigroups with fixed Frobenius number

TL;DR

This paper introduces a method to construct a rooted tree of irreducible numerical semigroups with a fixed Frobenius number, utilizing Kunz-coordinates vectors to facilitate the process.

Contribution

It provides a novel tree-based construction and a vector-based translation for analyzing irreducible numerical semigroups with a given Frobenius number.

Findings

Constructed a rooted tree structure for irreducible numerical semigroups

Translated the problem into manipulating 0-1 vectors

Facilitated analysis of semigroups with fixed Frobenius number

Abstract

In this paper we present a procedure to build the set of irreducible numerical semigroups with a fixed Frobenius number. The construction gives us a rooted tree structure for this set. Furthermore, by using the notion of Kunz-coordinates vector we translate the problem of finding such a tree into the problem of manipulating 0-1 vectors with as many component as the Frobenius number.