7,716 research outputs found
Proof of the Refined Alternating Sign Matrix Conjecture
Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the
number of alternating sign matrices of order equals . 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 column, equals . Standing on the
shoulders of A.G. Izergin, V. E. Korepin, and G. Kuperberg, and using in
addition orthogonal polynomials and -calculus, this stronger conjecture is
proved.Comment: Plain Te
Three Recitations on Holonomic Systems and Hypergeometric Series
A tutorial on what later became to be known as WZ theory, as well as a
motivated account of the seminal Gosper algorithm.Comment: Plain Te
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