Matthew Stamps: Betti numbers and anti-lecture hall compositions of random threshold graphs

Abstract

This talk will examine the one-to-one-to-one correspondence between threshold graphs, Betti numbers of quotients of polynomial rings with 2-linear resolutions, and anti-lecture hall compositions. I will present explicit combinatorial mappings between each of these families of objects and give formulas for the expected values of the Betti numbers and anti-lecture hall composition corresponding to a random threshold graph. This is joint work with Alex Engström and Christian Go.