Bijective Proofs of Gould's and Rothe's Identities

Details Bijective Proofs of Gould's and Rothe's Identities Bijective Proofs of Gould's and Rothe's Identities

2010-05-24

arxiv.org/abs/1005.4256v1

Discrete Math. 308 (2008), 1756--1759

Mathematics

Combinatorics

4 pages

Scientific paper

10.1016/j.disc.2007.04.020

We first give a bijective proof of Gould's identity in the model of binary
words. Then we deduce Rothe's identity from Gould's identity again by a
bijection, which also leads to a double-sum extension of the
$q$-Chu-Vandermonde formula.

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