Mathematics – Combinatorics
Scientific paper
2011-10-19
Mathematics
Combinatorics
One page. Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and this arxiv
Scientific paper
In 1996, my brilliant student John Noonan, discovered, and proved that there are 3(2n)!/(n(n+3)!(n-3)!) ways to line-up n people of different heights in such a way that out of the n(n-1)(n-2)/6 possible triples of people exactly one is such that the tallest stands (not necessarily immediately) in front of the second-tallest, who in turn, stands (not necessarily immediately) in front of the shortest. In that article, I promised a prize of 25 dollars for a nice combinatorial proof. Alex Burstein gave such a proof. On Oct. 14, 2011, I talked about Alex's lovely proof at the Howard U. math colloquium, and publicly presented the 25-dollar prize. The present note is the outcome. Congratulations Alex!
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