Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.02875 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917309337042944 |
|---|---|
| author | Zhang, Zhong-Xue |
| author_facet | Zhang, Zhong-Xue |
| contents | 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 $A$ and $B$. As an application, we present a bijective proof of a new identity involving the Eulerian polynomials of type $A$ and type $B$, solving a recent open problem proposed by Zhang. Additionally, we derive an identity between the half Eulerian polynomials of type $B$ and type $D$. Using this identity, we further obtain another relation about the Eulerian polynomials of type $A$ and type $B$, as well as a recursive formula connecting the restricted Eulerian polynomials of type $D$ and Eulerian polynomials of types $A$ and $B$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorial relations among restricted and half Eulerian polynomials of types $A$, $B$, and $D$ Zhang, Zhong-Xue Combinatorics 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 $A$ and $B$. As an application, we present a bijective proof of a new identity involving the Eulerian polynomials of type $A$ and type $B$, solving a recent open problem proposed by Zhang. Additionally, we derive an identity between the half Eulerian polynomials of type $B$ and type $D$. Using this identity, we further obtain another relation about the Eulerian polynomials of type $A$ and type $B$, as well as a recursive formula connecting the restricted Eulerian polynomials of type $D$ and Eulerian polynomials of types $A$ and $B$. |
| title | Combinatorial relations among restricted and half Eulerian polynomials of types $A$, $B$, and $D$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.02875 |