A symmetrical q-Eulerian identity

Details A symmetrical q-Eulerian identity A symmetrical q-Eulerian identity

2012-01-24

arxiv.org/abs/1201.4941v2

Mathematics

Combinatorics

S\'eminaire Lotharingien de Combinatoire, vol. 67(2012), Article B67c11 pages

Scientific paper

We find a $q$-analog of the following symmetrical identity involving binomial coefficients $\binom{n}{m}$ and Eulerian numbers $A_{n,m}$, 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.

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