Excedance numbers for permutations in complex reflection groups

TL;DR

This paper extends the study of excedance numbers in complex reflection groups, providing new results and correcting previous findings, thereby deepening understanding of permutation statistics in these algebraic structures.

Contribution

It generalizes the analysis of excedance numbers in complex reflection groups and corrects a previous result by Bagno, Garber, and Mansour.

Findings

Extended the distribution analysis of excedance numbers

Corrected a key previous result

Provided new formulas for involution statistics

Abstract

Recently, Bagno, Garber and Mansour studied a kind of excedance number on the complex reflection groups and computed its multidistribution with the number of fixed points on the set of involutions in these groups. In this note, we consider the similar problems in more general cases and make a correction of one result obtained by them.