Speaker: Iain Beaton (Acadia University)

Title: When are Graph Polynomials Unimodal?

Abstract: A graph polynomial is commonly a generating function which enumerates the number of subsets with a given property. Many of these properties are closed upwards, that is, any subset which contains a subset with that property also has that property. Some examples are the domination polynomial, zero-forcing polynomial, and dependent set polynomial. The coefficients of these polynomials can completely be determined by their respective minimal subsets, which form a clutter (or Sperner family). In this talk we focus on when a given polynomial, generated from a clutter, is unimodal. That is, the coefficients are non-decreasing and then non-increasing. This generalizes some known results and ties a common thread between each of these graph polynomials. We will also discuss how these results have made progress on the unimodality conjecture for the independence polynomial of trees.

July 16, 2026, 11:00 am-12:00 pm; Cass Science Hall, Room 101

All are welcome to attend.