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- W4287691938 abstract "A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. The size of its complement is called the genus and the largest number in the complement is called its Frobenius number. We consider the set of numerical semigroups with a fixed Frobenius number $f$ and analyse their genus. We find the asymptotic distribution of genus in this set of numerical semigroups and show that it is a product of a Gaussian and a power series. We show that almost all numerical semigroups with Frobenius number $f$ have genus close to $frac{3f}{4}$. We denote the number of numerical semigroups of Frobenius number $f$ by $N(f)$. While $N(f)$ is not monotonic we prove that $N(f)<N(f+2)$ for every $f$." @default.
- W4287691938 created "2022-07-26" @default.
- W4287691938 creator A5065125948 @default.
- W4287691938 date "2020-08-06" @default.
- W4287691938 modified "2023-10-15" @default.
- W4287691938 title "Distribution of genus among numerical semigroups with fixed Frobenius number" @default.
- W4287691938 doi "https://doi.org/10.48550/arxiv.2008.02963" @default.
- W4287691938 hasPublicationYear "2020" @default.
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