Statistics on Wreath Products

TL;DR

This paper develops methods for calculating generating functions of statistics over colored permutation groups, extending classical theorems from symmetric groups to these more general structures.

Contribution

It introduces generalized methods for statistics calculation and extends known symmetric group theorems to colored permutation groups.

Findings

Derived new formulas for generating functions in colored permutation groups

Extended classical symmetric group theorems to colored permutations

Provided computational techniques for permutation statistics

Abstract

We present methods of calculating statistics generating functions over the colored permutation groups, and generalizing known theorems from the symmetric groups to general colored permutations groups.