Bijections for an identity of Young Tableaux

By Amitai Regev and Doron Zeilberger

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Written: Feb. 22, 2010. Published in the Personal Journal of Ekhad and Zeilberger: May 2, 2010.
Exclusively published in the Personal Journal of Ekhad and Zeilberger and
It is nice to take a break, once-in-awhile, from heavy-duty computer-proofs, and prove cute little identities, using cute little bijective methods.
Added May 2, 2010: This little gem was submitted to the Notes Section of the American Mathematical Monthly, but stupidly rejected by them, because it was not "pretty" enough for the two referees, and because we didn't state the underlying (boring!) binomial coefficient identity. While beauty is in the eyes of the beholder, in our humble opinion it is much prettier than (at least) 99 percent of the notes published in the Monthly. Better luck next time, AMM!
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