A curious identity involving binomial coefficients
- A curious identity involving binomial coefficients
In combinatorics, a curious identity by Sun is the following combinatorial identity involving binomial coefficients first established by Zhi-Wei Sun in 2002:
:
After Sun's publication of this identity, five other proofs were obtained by various mathematicians. These include a WZ proof by Ekhad and Mohammed in 2003, and a nice combinatorial proof by Callan in 2004.
An application of the identity was given by Sun in a recent paper.
References
* D. Callan 2004. "A combinatorial proof of Sun's 'curious' identity", "Integers: Electronic Journal of Combinatorial Number Theory". Volume 4, #A05, 6 pp.
* S. B. Ekhad and M. Mohammed 2003. "A WZ proof of a 'curious' identity", "Integers: Electronic Journal of Combinatorial Number Theory". Volume 3, #A06, 2 pp.
* Zhi-Wei Sun 2002. "A curious identity involving binomial coefficients", "Integers: Electronic Journal of Combinatorial Number Theory". Volume 2, #A04, 8 pp.
* Zhi-Wei Sun 2008. "On sums of binomial coefficients and their applications", "Discrete Math". Volume 308, 4231–4245.
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