Geometry and Combinatorics Seminar (Math) - P. Deshpande

Speaker: Priyavrat Deshpande (Chennai Mathematical Institute)

"A statistic on labeled threshold graphs: interpreting coefficients of the threshold characteristic polynomial"

Consider the collection of hyperplanes in Rn whose defining equations are of the form xi+xj=0. This arrangement is called the threshold arrangement since its regions are in bijection with labeled threshold graphs on nn 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