## Abstract

We show that for every finite nonempty subset of ${\mathbb{N}}_{\ge 2}$ there are a numerical monoid *H* and a squarefree element $a\in H$ whose set of lengths $\U0001d5ab(a)$ is equal to *L*.

Show Summary Details# A realization theorem for sets of lengths in numerical monoids

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*Communications in Algebra*, 2019, Page 1*Journal of Algebra and Its Applications*, 2019, Page 2050137

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Get Access to Full TextWe show that for every finite nonempty subset of ${\mathbb{N}}_{\ge 2}$ there are a numerical monoid *H* and a squarefree element $a\in H$ whose set of lengths $\U0001d5ab(a)$ is equal to *L*.

Keywords: Numerical monoids; numerical semigroup algebras; sets of lengths; sets of distances

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**Received**: 2017-08-27

**Revised**: 2018-01-03

**Published Online**: 2018-02-07

**Published in Print**: 2018-09-01

**Funding Source: **Austrian Science Fund

**Award identifier / Grant number: **Project Number P 28864-N35

This work was supported by the Austrian Science Fund FWF, Project Number P 28864-N35.

**Citation Information: **Forum Mathematicum, Volume 30, Issue 5, Pages 1111–1118, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0180.

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[1]

Scott T. Chapman, Felix Gotti, and Marly Gotti

[2]

Felix Gotti

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