By Philip Matchett Wood and Doron Zeilberger
[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.
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Written: Jan. 25, 2007
Important: This article is accompanied by
Philip Matchett Wood's Maple packages.
Doron Zeilberger's List of Papers