Tutte polynomials of hyperplane arrangements and the finite field method

Abstract

This chapter discusses the Tutte polynomial of a hyperplane arrangement. This polynomial captures important enumerative, algebraic, and topological information about the arrangement. The chapter also describes the finite field method, a useful tool to compute Tutte polynomials of many graphs, matroids, and arrangements. Hyperplane arrangements and their complements. The characteristic and Tutte polynomials, and Tutte–Grothendieck invariants. Complements in https://www.w3.org/1998/Math/MathML"> ℝ , ℂ , F q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429161612/ab6e6aa5-46ff-432c-83f4-7ad3e3757dc3/content/math29_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> : regions, Poincaré polynomial, number of points. Topological and algebraic invariants of arrangements. The finite field method. Multivariate and arithmetic Tutte polynomials. Zonotopes and toric arrangements. The author was partially supported by NSF grants DMS-1600609 and DMS-1855610 and Simons Fellowship 613384.