A symmetrical q-Eulerian identity
Combinatorics
2012-04-02 v2
Abstract
We find a -analog of the following symmetrical identity involving binomial coefficients and Eulerian numbers , due to Chung, Graham and Knuth [{\it J. Comb.}, {\bf 1} (2010), 29--38]: {equation*} \sum_{k\geq 0}\binom{a+b}{k}A_{k,a-1}=\sum_{k\geq 0}\binom{a+b}{k}A_{k,b-1}. {equation*} We give two proofs, using generating function and bijections, respectively.
Cite
@article{arxiv.1201.4941,
title = {A symmetrical q-Eulerian identity},
author = {Guoniu Han and Zhicong Lin and Jiang Zeng},
journal= {arXiv preprint arXiv:1201.4941},
year = {2012}
}
Comments
S\'eminaire Lotharingien de Combinatoire, vol. 67(2012), Article B67c11 pages