Apéry sets of shifted numerical monoids

A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid \(S\), consider the family of "shifted" monoids \(M_n\) obtained by adding \(n\) to each generator of \(S\). In this paper, we characterize the Apéry set of \(M_n\) in terms of the Apéry set...

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Bibliographic Details
Published inarXiv.org
Main Authors O'Neill, Christopher, Pelayo, Roberto
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.04.2018
Subjects
Algorithms
Integers
Monoids
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Summary:A numerical monoid is an additive submonoid of the non-negative integers. Given a numerical monoid \(S\), consider the family of "shifted" monoids \(M_n\) obtained by adding \(n\) to each generator of \(S\). In this paper, we characterize the Apéry set of \(M_n\) in terms of the Apéry set of the base monoid \(S\) when \(n\) is sufficiently large. We give a highly efficient algorithm for computing the Apéry set of \(M_n\) in this case, and prove that several numerical monoid invariants, such as the genus and Frobenius number, are eventually quasipolynomial as a function of \(n\).
ISSN:2331-8422
DOI:10.48550/arxiv.1708.09527