Combinatorial relations among restricted and half Eulerian polynomials of types $A$, $B$, and $D$
Combinatorics
2026-03-04 v1
Abstract
In this paper, we study relations among several types of Eulerian polynomials from a combinatorial viewpoint. We establish an identity between the restricted Eulerian polynomials of types and . As an application, we present a bijective proof of a new identity involving the Eulerian polynomials of type and type , solving a recent open problem proposed by Zhang. Additionally, we derive an identity between the half Eulerian polynomials of type and type . Using this identity, we further obtain another relation about the Eulerian polynomials of type and type , as well as a recursive formula connecting the restricted Eulerian polynomials of type and Eulerian polynomials of types and .
Cite
@article{arxiv.2603.02875,
title = {Combinatorial relations among restricted and half Eulerian polynomials of types $A$, $B$, and $D$},
author = {Zhong-Xue Zhang},
journal= {arXiv preprint arXiv:2603.02875},
year = {2026}
}