__Claremont Graduate University__ | __Claremont McKenna__ | __Harvey Mudd__ | __Pitzer__ | __Pomona__ | __Scripps__

Proudly Serving Math Community at the Claremont Colleges Since 2007

Copyright © 2011 Claremont Center for the Mathematical Sciences

09/12/2017 - 12:15pm

09/12/2017 - 1:10pm

Speaker:

Chris O'Neill (UC Davis)

Abstract:

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.

Where:

Millikan 2099, Pomona College