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On integer partitions corresponding to numerical semigroups

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arxiv 2302.08391 v1 pith:PCJS6WVG submitted 2023-02-16 math.CO math.GRmath.NT

Hannah E. Burson , Hayan Nam , Simone Sisneros-Thiry This is my paper · ORCID
classification math.COmath.GRmath.NT
keywords numericalsemigroupspartitionsinjectionintegernumberadditiveappear
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Numerical semigroups are cofinite additive submonoids of the natural numbers. In 2011, Keith and Nath illustrated an injection from numerical semigroups to integer partitions. 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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