Joyal's Proof of Cayley's Formula
By Gyu Eun Lee and Doron Zeilberger
(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
and to check whether you got it right, check the
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
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Doron Zeilberger's Home Page