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Factorizations into irreducible numerical semigroups

Pedro A. Garcia-Sanchez

Abstract

Every numerical semigroup can be expressed as an intersection of irreducible numerical semigroups. We show that the unions of sets of lengths of factorizations of numerical semigroups into irreducible numerical semigroups are all equal to $\mathbb{N}_{\ge 2}$.

Factorizations into irreducible numerical semigroups

Abstract

Every numerical semigroup can be expressed as an intersection of irreducible numerical semigroups. We show that the unions of sets of lengths of factorizations of numerical semigroups into irreducible numerical semigroups are all equal to .

Paper Structure

This paper contains 3 sections, 5 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Unions of sets of lengths of factorizations
  3. Future work

Key Result

Lemma 1

Let $i$ be an odd positive integer.

Theorems & Definitions (10)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Corollary 3
  • proof
  • Lemma 4
  • proof
  • Theorem 5
  • Remark 6