A Very Short (Bijective!) Proof of Touchard's Catalan Identity

Amitai Regev, Nathaniel Shar, and Doron Zeilberger

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Posted: π Day, 2015

This version: March 24, 2015.

It is still fun to find bijective proofs of identities, even if they are shaloshable!

Added March 24, 2015: It turns out that our nice bijection was too nice not to have been known before. See the insightful comments by Dominique Gouyo-Beauchamp, Kyle Petersen, and Dennis Stanton.

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