# Reflexponents

## TL;DR

The paper introduces reflexponents, new invariants for reflection groups that generalize classical generating functions involving exponents, by incorporating orbits of reflecting hyperplanes, verified case-by-case.

## Contribution

It presents novel reflexponents as analogues to exponents, extending generating functions for reflection groups to include hyperplane orbits.

## Key findings

- Reflexponents generalize classical invariants for reflection groups.
- Verification is performed case-by-case.
- New generating functions are established using reflexponents.

## Abstract

Certain classical generating functions for elements of reflection groups can be expressed using fundamental invariants called exponents. We give new analogues of such generating functions that accommodate orbits of reflecting hyperplanes using similar invariants we call reflexponents. Our verifications are case-by-case.