New York Journal of Mathematics
Volume 2 (1996) 59-68


Doron Zeilberger

Proof of the Refined Alternating Sign Matrix Conjecture

Published: April 15, 1996
Keywords: enumeration, alternating sign matrices, square ice, Izergin-Korepin formula, orthogonal polynomials, q-analysis, q-Legendre polynomials, exactly solvable models
Subject: Primary: 05A; Secondary: 33

Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order $n$ 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 rth column equals
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.


Supported in part by the NSF.


Author information

Department of Mathematics, Temple University, Philadelphia, PA19122, USA
Current Address: Department of Mathematics, Rutgers University, Hill Center-Busch Campus, Piscataway, NJ 08854-8019, USA