Palindromicity of multivariate Eulerian polynomials

TL;DR

This paper generalizes the palindromic property of univariate Eulerian polynomials to multivariate cases, revealing new combinatorial identities through polynomial relations and permutation bijections.

Contribution

It introduces a multivariate extension of Eulerian polynomials and establishes their palindromic nature, along with deriving related combinatorial identities.

Findings

Multivariate Eulerian polynomials are palindromic.

New combinatorial identities are derived from polynomial relations.

A bijection between permutations underpins the proofs.

Abstract

We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted from this polynomial relation and the bijection between permutations involved in the proof of the identity.