Rarity of the infinite chains in the tree of numerical semigroups

Published 31 Jan 2024 in math.NT, cs.DM, and math.CO | (2401.18060v1)

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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