Cyclic sieving for generalised non-crossing partitions associated to complex reflection groups of exceptional type - the details

TL;DR

This paper proves two cyclic sieving phenomena for generalized non-crossing partitions linked to exceptional complex reflection groups, confirming conjectures and providing detailed computational evidence.

Contribution

It establishes the validity of two cyclic sieving phenomena for these partitions, supporting conjectures by Armstrong and Bessis-Reiner with detailed computations.

Findings

Confirmed two cyclic sieving phenomena for exceptional complex reflection groups

Provided computational details supporting the conjectures

Strengthened understanding of non-crossing partitions in complex reflection groups

Abstract

We prove that the generalised non-crossing partitions associated to well-generated complex reflection groups of exceptional type obey two different cyclic sieving phenomena, as conjectured by Armstrong, respectively by Bessis and Reiner. This manuscript accompanies the paper "Cyclic sieving for generalised non-crossing partitions associated to complex reflection groups of exceptional type" [arXiv:1001.0028], for which it provides the computational details.