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2017 The realization problem for delta sets of numerical semigroups
Stefan Colton, Nathan Kaplan
J. Commut. Algebra 9(3): 313-339 (2017). DOI: 10.1216/JCA-2017-9-3-313


The delta set of a numerical semigroup $S$, denoted $\Delta (S)$, is a factorization invariant that measures the complexity of the sets of lengths of elements in~$S$. We study the following problem: Which finite sets occur as the delta set of a numerical semigroup $S$? It is known that $\min \Delta (S) = \gcd \Delta (S)$ is a necessary condition. For any two-element set $\{d,td\}$ we produce a semigroup~$S$ with this delta set. We then show that, for $t\ge 2$, the set $\{d,td\}$ occurs as the delta set of some numerical semigroup of embedding dimension~3 if and only if $t=2$.


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Stefan Colton. Nathan Kaplan. "The realization problem for delta sets of numerical semigroups." J. Commut. Algebra 9 (3) 313 - 339, 2017.


Published: 2017
First available in Project Euclid: 1 August 2017

zbMATH: 06790173
MathSciNet: MR3685046
Digital Object Identifier: 10.1216/JCA-2017-9-3-313

Primary: 11B75 , 20M13 , 20M14

Keywords: delta set , factorization theory , non-unique factorization , numerical semigroup

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium


Vol.9 • No. 3 • 2017
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