The Combinatorics of Counting Faces of a Hyperplane Arrangement

Abstract: An arrangement of hyperplanes is a finite collection of hyperplanes in a vector space. In the case of a Euclidean space the arrangement describes a stratification where each stratum, also called a face, is a convex subset. It is a classical problem to determine the number of various-dimensional faces in terms of the combinatorics of intersection of hyperlpanes. In this talk I will focus on a class of arrangements called rational arrangements and explain the finite field method which helps count the codimension-$0$ strata. With the help of many examples I will demonstrate how various combinatorial techniques play an important role in this counting problem. This talk is self-contained and mainly a survey of interesting results in the field.

commutative algebraalgebraic topologycombinatorics

Audience: researchers in the topic

Applications of Combinatorics in Algebra, Topology and Graph Theory

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