Joyal's Proof of Cayley's Formula

By Gyu Eun Lee and Doron Zeilberger

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(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)

Written: July 16, 2012

André Joyal's seminal proof of Cayley's nn-2 formula is explained in detail to an undergraduate combinatorics class.
To test your understanding, try to answer the quiz, and to check whether you got it right, check the solution.
Added Aug. 6, 2012: I gave almost the same talk to the very talented students at 2012 Summer Mathematics Institute For Bright And Gifted Pre-College Students held at Oakland University, and taught by Eddie Cheng and Laszo Liptak. Here are the solutions once again, with the names of the people who got it completely right.
Added Aug. 12, 2012: Here is a beautiful SAGE implementation of the Joyal mapping written by Sebastien Labbé .

Added July 1, 2015: Here is a translation and adaptation, by Ron Holzman, in Hebrew .
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

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