Proof of the Refined Alternating Sign Matrix Conjecture

Details Proof of the Refined Alternating Sign Matrix Conjecture Proof of the Refined Alternating Sign Matrix Conjecture

1996-06-03

arxiv.org/abs/math/9606224v1

New York J. Math 2(1996), 59-68

Mathematics

Combinatorics

Plain TeX

Scientific paper

Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order $n$ equals $A(n):={{1!4!7! ... (3n-2)!} \over {n!(n+1)! ... (2n-1)!}}$. 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 $r^{th}$ column, equals $A(n) {{n+r-2} \choose {n-1}}{{2n-1-r} \choose {n-1}}/ {{3n-2} \choose {n-1}}$. 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.

Affiliated with

Also associated with

No associations

Rating

Proof of the Refined Alternating Sign Matrix Conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Proof of the Refined Alternating Sign Matrix Conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Proof of the Refined Alternating Sign Matrix Conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-184702