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Article Dans Une Revue Seminaire Lotharingien de Combinatoire Année : 2012

A symmetrical q-Eulerian identity

Guo-Niu Han

Résumé

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.

Dates et versions

hal-00843315 , version 1 (11-07-2013)

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Citer

Guo-Niu Han, Zhicong Lin, Jiang Zeng. A symmetrical q-Eulerian identity. Seminaire Lotharingien de Combinatoire, 2012, 67, pp.Article B67c. ⟨hal-00843315⟩
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