Proof of a Conjecture of Chan, Robbins, and Yuen.

By Doron Zeilberger

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Appearrd in Elec. Trans. of Numerical Analysis (ETNA), 9(1999), 147-148. [IWOP98 proceedings vol.] .

Written: Nov. 17, 1998.

Israel Gelfand once amused Dick Askey by calling him a combinatorialist. Dick always thought of himself as a hard-nosed analyst, and at the time only had one paper, with Mourad Ismail and Tom Koornwinder that may be termed combinatorics. But, a great man like Gelfand knows what he is talking about. The heritage of special functions, orthogonal polynomials and constant term identities, preached by Dick Askey and George Andrews, are starting to become indispensable tools in enumeration. So far, the work of two of Dick Askey's students was crucial to my work in enumeration. First came the work of Dennis Stanton, co-inventor of the Stanton-Stembridge trick, that was instrumental in my proof of the Alternating Sign Matrix Conjecture. Then came the work of Jim Wilson (and related work of George Andrews and Dick Askey) that was of fundamental importance in my proof of the Refined Alternating Sign Matrix Conjecture (by the way, both these conjectures were posed by Mills, (the same!) Robbins, and Rumsey). In this article, it is the turn of yet another Askey student to be in the limelights: Chip Morris.

Added Jan. 25, 2000: I just came back from the AMS Annual meeting, and was told by Richard Stanley that Dave Robbins is not convinced by the succinct treatment of this article, and needs more details. Worse, he succeeded in inflicting these doubts on Richard. On the urging of Richard Stanely, I wrote Dave and Richard an explanation with a Detailed Sketch of the Details of the proof of (Chip)
Added Nov. 2003: Sadly, Dave Robbins passed away in Sept. 2003. It was a terrible loss both to `outside' and `inside' mathematics.

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