# Equidistributions of Mahonian statistics over pattern avoiding permutations

## TL;DR

This paper studies Mahonian statistics, specifically Mahonian 3-functions, and proves their equidistribution over pattern-avoiding permutations using combinatorial tools like block decomposition, Dyck paths, and generating functions.

## Contribution

It extends the classification of Mahonian 3-functions and establishes new equidistribution results over pattern-avoiding permutations.

## Key findings

- Mahonian 3-functions are equidistributed over certain pattern-avoiding sets
- Utilizes combinatorial tools such as block decomposition and Dyck paths
- Provides new insights into Mahonian statistics and their distributions

## Abstract

A Mahonian d-function is a Mahonian statistic that can be expressed as a linear combination of vincular pattern statistics of length at most d. Babson and Steingrimsson classified all Mahonian 3-functions up to trivial bijections and identified many of them with well-known Mahonian statistics in the literature. We prove a host of Mahonian 3-function equidistributions over pattern avoiding sets of permutations. Tools used include block decomposition, Dyck paths and generating functions.