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arXiv · 2401.18060

Rarity of the infinite chains in the tree of numerical semigroups

Maria Bras-Amorós·Mariana Rosas Ribeiro
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Abstract

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

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Maria Bras-Amorós, Mariana Rosas Ribeiro. 2024-01-31. Rarity of the infinite chains in the tree of numerical semigroups. https://arxiv.org/abs/2401.18060

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