2.00 pm, Seminar Hall
Computation of the characteristic polynomial of certain threshold arrangements
Balasubramanian A.R.
Chennai Mathematical Institute.
19-03-19

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Abstract

An arrangement of hyperplanes is a finite collection of hyperplanes in a real Euclidean space. To such a collection one associates the characteristic polynomial that encodes the combinatorics of intersections of hyperplanes. The problem of finding the characteristic polynomial of Shi threshold and Catalan threshold arrangements was a well known open problem in Stanley's list of problems. Seunghyun Seo solved both the problems by clever arguments using the finite field method. However, in his paper, he left open the problem of computing the characteristic polynomial of a broader class of threshold arrangements. In this talk, I will present a method for computing the characteristic polynomial of this family of arrangements. To keep the presentation simple, I will first discuss the solution for an easier subfamily. Time permitting, I will sketch a solution of the general case.