Counting descent pairs with prescribed colors in the colored permutation groups

TL;DR

This paper introduces new (c, d)-descent statistics for colored permutation groups, deriving their distributions using combinatorial methods, recurrences, and generating functions.

Contribution

It defines and analyzes (c, d)-descents in colored permutation groups, providing new combinatorial formulas and distribution results.

Findings

Distribution formulas for (c, d)-descents in Z_r w S_n

Use of recurrences and generating functions in analysis

New combinatorial insights into colored permutation statistics

Abstract

We define new statistics, (c, d)-descents, on the colored permutation groups Z_r \wr S_n and compute the distribution of these statistics on the elements in these groups. We use some combinatorial approaches, recurrences, and generating functions manipulations to obtain our results.