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# Forum Mathematicum

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Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 30, Issue 5

# A realization theorem for sets of lengths in numerical monoids

Alfred Geroldinger
• Corresponding author
• Institute for Mathematics and Scientific Computing, University of Graz, NAWI Graz, Heinrichstraße 36, 8010 Graz, Austria
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• Other articles by this author:
/ Wolfgang Alexander Schmid
• Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8, CNRS, UMR 7539, F-93526, Saint-Denis, France
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Published Online: 2018-02-07 | DOI: https://doi.org/10.1515/forum-2017-0180

## Abstract

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

MSC 2010: 20M13; 20M14

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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,

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