The refined alternating sign matrix conjecture states that the numerators and denominators obtained by taking the ratios of
adjacent terms in the triangular array of the number of 
"bordered" alternating
sign matrices 
with a 1 at the top of column 
are, respectively, the numbers in the (2, 1)- and (1, 2)-Pascal
triangles which are different from 1. This conjecture was proven by Zeilberger (1996).
Refined Alternating Sign Matrix Conjecture
See also
Alternating Sign Matrix, Alternating Sign Matrix ConjectureExplore with Wolfram|Alpha
References
Bressoud, D. and Propp, J. "How the Alternating Sign Matrix Conjecture Was Solved." Not. Amer. Math. Soc. 46, 637-646.Zeilberger, D. "Proof of the Refined Alternating Sign Matrix Conjecture." New York J. Math. 2, 59-68, 1996.Referenced on Wolfram|Alpha
Refined Alternating Sign Matrix ConjectureCite this as:
Weisstein, Eric W. "Refined Alternating Sign Matrix Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RefinedAlternatingSignMatrixConjecture.html