Time: 09:30
Speaker: Priyavrat Deshpande (Chennai Mathematical Institute)
Title: "A statistic on labeled threshold graphs: interpreting coefficients of the threshold characteristic polynomial"
Room: Zoom

Abstract: Consider the collection of hyperplanes in $\mathbb{R}^n$ whose defining equations are of the form $x_i + x_j =0$. This arrangement is called the threshold arrangement since its regions are in bijection with labeled threshold graphs on $n$ vertices. Zaslavsky's theorem implies that the number of regions is the sum of coefficients of the characteristic polynomial of the arrangement. In this talk I will explain how to give a combinatorial meaning to these coefficients as the number of labeled threshold graphs with a certain property, thus answering a question posed by Stanley. This talk is based on joint work with Krishna Menon and Anurag Singh