Shows that most numerical semigroups have finite descendants, suggesting insights into their structure.
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.
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Bras-Amorós et al. (2026) studied this question.
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