Fibonacci-like behavior of the number of numerical semigroups of a given genus
By Maria Bras-Amorós. 2008
126 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/03d6a7171e8820697822b038b77aef5bed2235ff
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Statistical and Nonlinear Physics
Citations in the corpus
- Wilf’s conjecture and Macaulay’s theorem (2017, methodology): “Wilf’s conjecture has been shown to hold under various hypotheses, including in [22] for e = 2 as mentioned above, in [8] for e = 3, in [7] for |L| ≤ 4, by computer in [2] for genus g ≤ 50 and more recently in [10] for g ≤ 60, in [11] for c ≤ 2m, and in [19] for e ≥ m/2 and for m ≤ 8.”
- Fibonacci-like growth of numerical semigroups of a given genus (2011, background): “It was observed by BrasAmorós [2] that ng exhibits Fibonacci-like growth; in particular, it was conjectured that limg→∞ ng+1 ng = ϕ, where ϕ = 1+ √ 5 2 is the golden ratio.”
- Constructing numerical semigroups of a given genus (2009, methodology): “M. Bras-Amorós, Fibonacci-like behavior of the number of numerical semigroups of a given genus, Semigroup Forum 76 (2008), no. 2, 379–384.”
- Counting numerical semigroups by genus and some cases of a question of Wilf (2012, methodology): “For example, the semigroup 〈13, 14, 15, 16, 17, 18, 20, 22, 23〉 has 16 gaps, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 19, 21, 24, 25}, and the 2-fold sum of these gaps is [2, 50]\{39, 41, 47}.”