Constructing Numerical Semigroups of a Given Genus

Abstract

Let n_g denote the number of numerical semigroups of genus g. Bras-Amoros conjectured that n_g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree. We offer a new, simpler approach to counting numerical semigroups of a given genus. Our method gives direct constructions of families of numerical semigroups, without referring to the generators or the semigroup tree. In particular, we give an improved asymptotic lower bound for n_g.

11 pages, 3 figures, 2 tables; accepted by Semigroup Forum

References in corpus (3)

• Fibonacci-Like Behavior of the Number of Numerical Semigroups of a Given Genus
• Computing the number of numerical semigroups using generating functions
• Improved bounds on the number of numerical semigroups of a given genus

Cited by in corpus (10)

• Counting Numerical Semigroups
• Sets Characterized by Missing Sums and Differences
• Gapsets and numerical semigroups
• The Proportion of Weierstrass Semigroups
• Degree asymptotics of the numerical semigroup tree
• Numerical semigroups problem list
• Sub-Fibonacci behavior in numerical semigroup enumeration
• Trimming the numerical semigroups tree to probe Wilf's conjecture to higher genus
• Fibonacci-like growth of numerical semigroups of a given genus
• Kunz languages for numerical semigroups are context sensitive