Random numerical semigroups

09/12/2017 - 12:15pm
09/12/2017 - 1:10pm
Chris O'Neill (UC Davis)

A numerical semigroup is a subset of the natural numbers that is closed under addition. Consider a numerical semigroup S selected via the following random process: fix a probability p and a positive integer M, and select a generating set for S from the integers 1,...,M where each potential generator has probability p of being selected. What properties can we expect the numerical semigroup S to have? For instance, when do we expect S to contain all but finitely many positive integers, and how many minimal generators do we expect S to have? In this talk, we answer several such questions, and describe some surprisingly deep combinatorial structures that naturally arise in the process. No familiarity with numerical semigroups or probability will be assumed for this talk.

Millikan 2099, Pomona College