Rarity of the infinite chains in the tree of numerical semigroups

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...

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Published in:arXiv.org 2024-01
Main Authors: Bras-Amorós, Maria, Mariana Rosas Ribeiro
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Semigroups
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description 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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title Rarity of the infinite chains in the tree of numerical semigroups
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