Semigroup Forum

, Volume 76, Issue 2, pp 379–384

Fibonacci-like behavior of the number of numerical semigroups of a given genus

Research problem

DOI: 10.1007/s00233-007-9014-8

Cite this article as:
Bras-Amorós, M. Semigroup Forum (2008) 76: 379. doi:10.1007/s00233-007-9014-8

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.

Keywords

Numerical semigroup Fibonacci sequence Genus Wilf conjecture 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Universitat Rovira i VirgiliTarragonaSpain