Gapsets and numerical semigroups

Abstract

For g $\ge$ 0, let n g denote the number of numerical semi-groups of genus g. A conjecture by Maria Bras-Amorós in 2008 states that the inequality n g $\ge$ n g--1 + n g--2 should hold for all g $\ge$ 2. Here we show that such an inequality holds for the very large subtree of numerical semigroups satisfying c $\le$ 3m, where c and m are the conductor and multiplicity, respectively. Our proof is given in the more flexible setting of gapsets, i.e. complements in N of numerical semigroups.

References in corpus (5)

• Fibonacci-Like Behavior of the Number of Numerical Semigroups of a Given Genus
• Counting Numerical Semigroups
• Near-misses in Wilf's conjecture
• On a conjecture of Wilf about the Frobenius number
• The tree of numerical semigroups with low multiplicity

Cited by in corpus (7)

• A graph-theoretic approach to Wilf's conjecture
• Sub-Fibonacci behavior in numerical semigroup enumeration
• Almost symmetric numerical semigroups with high type
• Trimming the numerical semigroups tree to probe Wilf's conjecture to higher genus
• Counting numerical semigroups by Frobenius number, multiplicity, and depth
• A generalization of a theorem about gapsets with depth at most three
• Ordinarization numbers of numerical semigroups