Translator Disclaimer
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

Abstract

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 $t=2$.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 11B75, 20M13, 20M14

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
27 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.9 • No. 3 • 2017
Back to Top