By Stavros Garoufalidis, Thang TQ Le, Doron Zeilberger
Appeared in Proc. Natl. Acad. of Sci. (PNAS) v. 103 (2006), No. 38 (Sept. 19), 13928-13931.
First Written: March 25, 2003.
Revised and Corrected Version: Oct. 8, 2004.
My second postdoctoral position was spent, in the AY 1978-1979, at Georgia Tech. During that year I wrote the article "The algebra of linear partial difference operators and its applications". It was inspired by I.J. Good's "proof from the book" of the Dyson conjecture, and put it in the context of difference operators, and tried to show its potential importance.
I sent copies to Andrews, Askey, Dyson, Good, and Riordan. While they all gave me polite responses, the only one who really liked it was I.J. Good. Also the Math Review by Dick Askey was on the lukewarm side. One of the criticisms, by George Andrews, was that the "q-analog" of MacMahon's Master Theorem, was indeed a `q-analog', but not the kind he meant, and it seems not to be useful for q-series.
George may have been right about the particular q-analog that I proposed there, but I was recently vindicated in my gut feeling that the paper was "important", since the method introduced there proved crucial for the present paper, that proves a beautiful and natural quantum analog, conjectured by Stavros Garoufalidis and Thang Le, that according to them has important potential applications in knot theory.
It is an amusing fact that Stavros is now at Georgia Tech, that became a much better department since my time.
Doron Zeilberger's Home Page