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 Conjecture## Explore 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 Conjecture## Cite this as:

Weisstein, Eric W. "Refined Alternating Sign Matrix Conjecture." From *MathWorld*--A Wolfram Web Resource.
https://mathworld.wolfram.com/RefinedAlternatingSignMatrixConjecture.html