Rarity of the infinite chains in the tree of numerical semigroups

Identificador:  imarina:9633048

Handle: https://hdl.handle.net/20.500.11797/imarina9633048

Autores:  Bras-Amorós M; Rosas-Ribeiro M

Resumen:
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.