Bounds on the Number of Numerical Semigroups of a Given Genus

Abstract

Combinatorics on multisets is used to deduce new upper and lower bounds on the number of numerical semigroups of each given genus, significantly improving existing ones. In particular, it is proved that the number $n_g$ of numerical semigroups of genus $g$ satisfies $2F_g\le n_g\le 1+3\cdot 2^{g-3}$, where $F_g$ denotes the $g$th Fibonacci number.

References in corpus (1)

• Representation of Numerical Semigroups by Dyck Paths