Signed mahonians on some trees and parabolic quotients

TL;DR

This paper investigates the distribution of signed major and flag-major indices on certain algebraic structures, extending previous results and revealing simple factorization formulas for these distributions.

Contribution

It generalizes and extends prior work on major index distributions to new classes of groups and combinatorial structures, including parabolic quotients and special trees called rakes.

Findings

Distribution formulas have simple factorizations.

Extended results to wreath products and related groups.

Unified approach to major index distributions across structures.

Abstract

We study the distribution of the major index with sign on some parabolic quotients of the symmetric group, extending and generalizing simultaneously results Gessel-Simion and Adin-Gessel-Roichman, and on some special trees that we call rakes. We further consider and compute the distribution of the flag-major index on some parabolic quotients of wreath products and other related groups. All these distributions turn out to have very simple factorization formulas.