Computing the Tutte polynomial of a hyperplane arragement

Federico Ardila

Vol. 230 (2007), No. 1, 1–26

DOI: 10.2140/pjm.2007.230.1

Abstract

We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing the Tutte polynomial by solving a related enumerative problem. As a consequence, we obtain new formulas for the generating functions enumerating alternating trees, labelled trees, semiorders and Dyck paths.

Keywords

hyperplane arrangement, Tutte polynomial, finite field method

Mathematical Subject Classification 2000

Primary: 52C35

Secondary: 05B35, 05A15

Milestones

Received: 10 September 2004

Accepted: 20 February 2007

Published: 1 March 2007