Fibonacci-like growth of numerical semigroups of a given genus

Semigroup Forum, Volume 86, Issue 3, 2011, Pages 634-662.

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Abstract:

We give an asymptotic estimate of the number of numerical semigroups of a given genus. In particular, if $n_g$ is the number of numerical semigroups of genus $g$, we prove that $n_g$ tends to $S \phi^g$, where $\phi$ is the golden ratio, and $S$ is a constant, resolving several related conjectures concerning the growth of $n_g$. In addi...More

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