Rarity of the infinite chains in the tree of numerical semigroups

Semigroup Forum 2026 Open access

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Authors: Maria Bras-Amorós, Mariana Rosas Ribeiro
DOI: 10.1007/s00233-026-10661-3
Cited by: 0
References: 22

Abstract

Abstract We prove that, for each fixed genus, the proportion of semigroups of that genus belonging to infinite chains in the semigroup tree approaches 0 as the genus grows to infinity. This means that most numerical semigroups have a finite number of descendants in the semigroup tree. This problem has been open since 2009.

Fields of Study & Subjects

Polynomial and algebraic computation Commutative Algebra and Its Applications Rough Sets and Fuzzy Logic

Publication details

Journal / source
Semigroup Forum
Publisher
Springer Science and Business Media LLC
Volume
113
Issue
2
Pages
640-645
Publication date
10 August 2026
Language
EN