Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the
number of alternating sign matrices of order n equals A(n):=n!(n+1)!...(2nβ1)!1!4!7!...(3nβ2)!β. Mills, Robbins, and Rumsey also made
the stronger conjecture that the number of such matrices whose (unique) `1' of
the first row is at the rth column, equals A(n)(nβ1n+rβ2β)(nβ12nβ1βrβ)/(nβ13nβ2β). Standing on the
shoulders of A.G. Izergin, V. E. Korepin, and G. Kuperberg, and using in
addition orthogonal polynomials and q-calculus, this stronger conjecture is
proved.Comment: Plain Te