Semigroup Forum

, Volume 80, Issue 2, pp 242–254

Constructing numerical semigroups of a given genus

Research Article

Abstract

Let ng denote the number of numerical semigroups of genus g. Bras-Amorós conjectured that ng 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 ng.

Keywords

Numerical semigroup Fibonacci number Genus 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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