Bounds on the Number of Numerical Semigroups of a Given Genus

2008/02/15 by Maria Bras-Amorós, Maria Bras-Amoros, Bras-Amoros, Maria · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #cs.DM #math.CO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0802.2175

arxiv created 2008/02/15 · arxiv updated 2009/12/01

Abstract

Combinatorics on multisets is used to deduce new upper and lower bounds on the number of numerical semigroups of each given genus, significantly improving existing ones. In particular, it is proved that the number n_g of numerical semigroups of genus g satisfies 2F_g≤ n_g≤ 1+3⋅ 2^g-3, where F_g denotes the gth Fibonacci number.

Cited by

• Ordinarization numbers of numerical semigroups

Related

• Improved bounds on the number of numerical semigroups of a given genus
• Fibonacci-like growth of numerical semigroups of a given genus
• Counting numerical semigroups by genus and even gaps
• Computing the number of numerical semigroups using generating functions
• Algorithms and results on multiparameter counting of numerical semigroups