A Translation Method for Finding Combinatorial Bijections

By Philip Matchett Wood and Doron Zeilberger

Written: Jan. 25, 2007

[Appeared in Annals of Combinatorics 13(2009), 383-402.]

During the Renaissance, solving cubic and quartic equations was a professional sport, and mathematical "athletes" made a living competing to solve them. Then the secret was given away by Cardano, and some people lost a source of income, and probably were mad at him.

Nowadays, quite a few combinatorialists make a living by finding "elegant" bijective proofs of algebraic or combinatorial identities. Some of them probably have some trade secrets that they didn't tell anyone. In this article we reveal our own secrets, and hope that no one will get mad at us, since the "translation method" is really more like a methodology, and there is still room for human creativity.

Important: This article is accompanied by Philip Matchett Wood's Maple packages.
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