On Integer Partitions Corresponding to Numerical Semigroups

Hannah E. Burson; Hayan Nam; Simone Sisneros-Thiry

doi:10.1007/s00025-023-01974-8

On Integer Partitions Corresponding to Numerical Semigroups

Hannah E. Burson, Hayan Nam, Simone Sisneros-Thiry

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	193
Journal	Results in Mathematics
Volume	78
Issue number	5
DOIs	https://doi.org/10.1007/s00025-023-01974-8
State	Published - Oct 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Frobenius number
Partitions
genus
multiplicity
numerical semigroups

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10.1007/s00025-023-01974-8

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N2 - 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.

AB - 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.

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KW - genus

KW - multiplicity

KW - numerical semigroups

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ER -

On Integer Partitions Corresponding to Numerical Semigroups

Abstract

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Keywords

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