Algebra & Geometry Seminar
Algebra & Geometry Seminar
Date: 01/10/2025 Time: 14.15 Room: 715
Title: Numerical semigroup tree: type-representation
Abstract: The numerical semigroups can be organized as the nodes of an infinite rooted tree, where
the root corresponds to the set of all nonnegative integers and the more elements we remove from a numerical semigroup, the farther we get from the root. Several conjectures circulate already about the magnitude of the growth of this tree.
We suggest to refine the information by taking into account also the type of the semigroups. We found that the number of semigroups of genus g and type t is constant when t is close to g, while g grows. We also study the unimodality of various sequences, as well as the behavior of the leaves in the semigroup tree. We put forward several conjectures that are supported by various computational experiments.
This is joint work with Jonathan Chappelon and Jorge Ramirez Alfonsin.