By Doron Zeilberger

.pdf .ps .tex

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.

Doron Zeilberger's List of Papers