A Proof Of George Andrews' and David Robbins' q-TSPP Conjecture

By Christoph Koutschan, Manuel Kauers, and Doron Zeilberger

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Appeared in the Proceedings of the National Academy of Science, v. 108, no. 6 (Feb. 8, 2011), 2196-2199.

First Written: Feb. 23, 2010.

About a year-and-a-half ago, Manuel Kauers, Christoph Koutschan, and I gave a beautiful semi-rigorous proof of the famous q-TSPP conjecture that failed to impress anyone. We realized that mathematicians do not care about "truth", they only care about that artificial art-form called "rigorous proof". In order to humor them, we (or rather Christoph Koutschan) worked very hard to turn this semi-rigorous proof into a fully rigorous proof. This was a true computational tour-de-force on his part, requiring brilliant human insight, and lots of sneaky tricks, to tame the computer to reduce a computation, that on the face of it, looked like it would take fifty years on a future computer, to a computation that only took a couple of weeks on a medium-size contemporary computer. It is a real breakthrough, if we say so ourselves, not only in combinatorics, but also in symbolic computation, and a great victory of my beloved holonomic ansatz.

Very Important

This article is accompanied by supporting software and data.

Added Jan. 25, 2011: This was written up in the Austrian media.

ajouté Fév. 4, 2011: en francais (par Maurice Mashaal, rédacteur en chef de Pour la Science).

Added March 2, 2011: We are also famous in Switzerland! Read George Szpiro's wonderful article (that its global and universal truths make-up for some local inaccuracies, see my Email message to Christoph Koutschan and Manuel Kauers).

Added March 8, 2011: Read Tony Philips's take on math-in-the-media and Allyn Jackson's summary .

Added Nov. 2015: This article was the David P. Robbins prize of the American Mathematical Society

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