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Constructing numerical semigroups of a given genus

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Abstract

Let n g denote the number of numerical semigroups of genus g. Bras-Amorós conjectured that n g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree. We offer a new, simpler approach to counting numerical semigroups of a given genus. Our method gives direct constructions of families of numerical semigroups, without referring to the generators or the semigroup tree. In particular, we give an improved asymptotic lower bound for n g .

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Yufei Zhao

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  1. Yufei Zhao
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Correspondence to Yufei Zhao.

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Communicated by J. Almeida.

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Zhao, Y. Constructing numerical semigroups of a given genus. Semigroup Forum 80, 242–254 (2010). https://doi.org/10.1007/s00233-009-9190-9

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  • DOI: https://doi.org/10.1007/s00233-009-9190-9

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