Computing the Tutte polynomial of a hyperplane arrangement

Details Computing the Tutte polynomial of a hyperplane arrangement Computing the Tutte polynomial of a hyperplane arrangement

2004-09-13

arxiv.org/abs/math/0409211v1

Mathematics

Combinatorics

27 pages, 2 figures

Scientific paper

We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arrangements, the computation of Tutte polynomials is then reduced to certain related enumerative questions. As a consequence, we obtain new formulas for the generating functions enumerating alternating trees, labelled trees, semiorders and Dyck paths.

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