Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903193 | Discrete Mathematics | 2017 | 11 Pages |
Abstract
Let ng be the number of numerical semigroups of genus g. We present an approach to compute ng by using even gaps, and the question: Is it true that ng+1>ng? is investigated. Let Nγ(g) be the number of numerical semigroups of genus g whose number of even gaps equals γ. We show that Nγ(g)=Nγ(3γ) for γâ¤âgâ3â and Nγ(g)=0 for γ>â2gâ3â; thus the question above is true provided that Nγ(g+1)>Nγ(g) for γ=âgâ3â+1,â¦,â2gâ3â. We also show that Nγ(3γ) coincides with fγ, the number introduced by Bras-Amorós (2012) in connection with semigroup-closed sets. Finally, the stronger possibility fγâ¼Ï2γ arises being Ï=(1+5)â2 the golden number.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Matheus Bernardini, Fernando Torres,