Tutte polynomials of hyperplane arrangements and the finite field method

2017/10/04 by Federico Ardila, Ardila, Federico
Engineering · Materials Science · Mathematics · #05A15 #11T99 #52B40 #52C35 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Liquid Crystal Research Advancements #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1710.01424

openalex publication_date 2017/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Tutte polynomial is a fundamental invariant associated to a graph, matroid, vector arrangement, or hyperplane arrangement. This short survey focuses on some of the most important results on Tutte polynomials of hyperplane arrangements. We show that many enumerative, algebraic, geometric, and topological invariants of a hyperplane arrangement can be expressed in terms of its Tutte polynomial. We also show that, even if one is only interested in computing the Tutte polynomial of a graph or a matroid, the theory of hyperplane arrangements provides a powerful finite field method for this computation.

Related

• Computing the Tutte polynomial of a hyperplane arrangement
• Tutte Polynomials of Symmetric Hyperplane Arrangements
• The Tutte Polynomial of Symmetric Hyperplane Arrangements
• The arithmetic Tutte polynomials of the classical root systems
• Tutte Polynomial of Ideal Arrangement