Proof of Kyle Petersen's Amazing Conjecture Relating the q- and Fibonacci Analogs of n!

By Doron Zeilberger

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Written: May 11, 2014

[Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger]

I just came back from the Ira Gessel 2015 conference, where three of Ira's brilliant students gave great talks. The first talk was by Kyle Petersen, and the same Kyle conjectured an amazing relation between the q- and Fibonacci analogs of n!, that he told Richard Stanley, who told me, during the banquet honoring Ira. The proof turned out to be not that hard, but nevertheless, almost as pretty as the statement.
Added May 13, 2015: Richard Stanley found an even nicer proof, see his Email message.

Added June 1, 2015: Johann Cigler found a yet nicer proof, see this gem.

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