On the Enumeration of the Set of Numerical Semigroups with Fixed Frobenius Number and Fixed Number of Second Kind Gaps

We study how certain invariants of numerical semigroups relate to the number of second kind gaps. Furthermore, given two fixed non-negative integers F and k , we provide an algorithm to compute all the numerical semigroups whose Frobenius number is F and which have exactly k second kind gaps.

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Bibliographic Details
Published inResultate der Mathematik Vol. 77; no. 1
Main Authors Robles-Pérez, Aureliano M., Rosales, José Carlos
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2022
Subjects
Mathematics
Mathematics and Statistics
11Y16
20M14
Irreducible numerical semigroups
Frobenius number
Wilf’s conjecture
second kind gaps
trees
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Summary:We study how certain invariants of numerical semigroups relate to the number of second kind gaps. Furthermore, given two fixed non-negative integers F and k , we provide an algorithm to compute all the numerical semigroups whose Frobenius number is F and which have exactly k second kind gaps.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-021-01542-y