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On Integer Partitions Corresponding to Numerical Semigroups

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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.

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Acknowledgements

We appreciate the referee for helpful feedback and carefully reading our paper. This material is based upon work supported by the National Science Foundation under Grant No. 1440140, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the summer of 2022. This work is supported by Korea Institute for Advanced Study (KIAS) grant funded by the Korea government. Hayan Nam was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1F1A1062319).

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, Twin Cities, Minneapolis, MN, 55455, USA

    Hannah E. Burson

  2. Department of Mathematics, Duksung Women’s University, Seoul, Republic of Korea

    Hayan Nam

  3. Department of Mathematics, California State University, East Bay, Hayward, CA, 94542, USA

    Simone Sisneros-Thiry

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  1. Hannah E. Burson
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  2. Hayan Nam
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Correspondence to Hayan Nam.

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Burson, H.E., Nam, H. & Sisneros-Thiry, S. On Integer Partitions Corresponding to Numerical Semigroups. Results Math 78, 193 (2023). https://doi.org/10.1007/s00025-023-01974-8

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