On Integer Partitions Corresponding to Numerical Semigroups

Numerical semigroups are cofinite additive submonoids of the natural numbers. Keith and Nath illustrated an injection from numerical semigroups to integer partitions (Keith and Nath in J Comb Number Theory 3(1):39–50, 2011). We explore this connection between partitions and numerical semigroups with...

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Bibliographic Details
Published in:Resultate der Mathematik Vol. 78; no. 5; p. 193
Main Authors: Burson, Hannah E., Nam, Hayan, Sisneros-Thiry, Simone
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.10.2023
Springer Nature B.V
Subjects:
Boxes
Integers
Mathematics
Mathematics and Statistics
Number theory
Semigroups
numerical semigroups
11P81
multiplicity
Partitions
genus
20M14
Frobenius number
05A17
ISSN:1422-6383, 1420-9012
Online Access:Get full text
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Summary:Numerical semigroups are cofinite additive submonoids of the natural numbers. Keith and Nath illustrated an injection from numerical semigroups to integer partitions (Keith and Nath in J Comb Number Theory 3(1):39–50, 2011). We explore this connection between partitions and numerical semigroups with a focus on classifying the partitions that appear in the image of the injection from numerical semigroups. In particular, we count the number of partitions that correspond to numerical semigroups in terms of genus, Frobenius number, and multiplicity, with some restrictions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-023-01974-8