The Tutte Polynomial of Complex Reflection Groups

TL;DR

This paper calculates the Tutte polynomial for hyperplane arrangements linked to complex reflection groups, utilizing formulas from De Concini and Procesi and insights into the normalisers of parabolic subgroups.

Contribution

It provides the first explicit computation of the Tutte polynomial for these arrangements, combining algebraic and combinatorial methods.

Findings

Explicit formulas for Tutte polynomials of complex reflection group arrangements

Connections established between algebraic structures and combinatorial invariants

New computational techniques for hyperplane arrangements in complex reflection groups

Abstract

This article computes the Tutte polynomial of the hyperplane arrangements associated to the complex reflection groups. The calculations are based on both formulas of De Concini and Procesi for Tutte polynomial and the normaliser of parabolic subgroups in complex reflection groups determined by Krishnasamy and Taylor.