TL;DR
This paper introduces a new proof for the asymptotic count of numerical semigroups of a given genus using compositions, and explicitly describes the associated constant.
Contribution
It provides a novel proof leveraging compositions and explicitly characterizes the asymptotic constant for numerical semigroups.
Findings
New proof for the asymptotic number of numerical semigroups
Explicit description of the asymptotic constant C
Simplification of the theory using compositions
Abstract
The use of compositions simplifies some aspects of the theory of numerical semigroups. We illustrate this by giving a new proof for the asymptotic number C((1 + \sqrt 5)/2) g of numerical semigroups of genus g and by describing the constant C explicitly 1 .
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Taxonomy
TopicsScheduling and Timetabling Solutions · Commutative Algebra and Its Applications · Advanced Optimization Algorithms Research