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Bounds on the Number of Numerical Semigroups of a Given Genus
Published 15 Feb 2008 in math.CO and cs.DM | (0802.2175v1)
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 $2F_{g}\leq n_g\leq 1+3\cdot 2{g-3}$, where $F_g$ denotes the $g$th Fibonacci number.
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