Fibonacci-Like Behavior of the Number of Numerical Semigroups of a Given Genus

Abstract

We conjecture a Fibonacci-like property on the number of numerical semigroups of a given genus. Moreover we conjecture that the associated quotient sequence approaches the golden ratio. The conjecture is motivated by the results on the number of semigroups of genus at most 50. The Wilf conjecture has also been checked for all numerical semigroups with genus in the same range.

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• On a conjecture of Wilf about the Frobenius number
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• Almost symmetric numerical semigroups with high type
• Infinite chains in the tree of numerical semigroups
• Generalized Numerical semigroups up to isomorphism
• A generalization of a theorem about gapsets with depth at most three
• Counting numerical semigroups by genus and even gaps via Kunz-coordinate vectors
• Ordinarization numbers of numerical semigroups
• Counting numerical semigroups by Frobenius number, multiplicity, and depth