By Arvind Ayyer and Doron Zeilberger
Written: Dec. 2, 2008.
The Razumov-Stroganov Conjecture is one of the most intriguing open problems in mathematics.
Alas, its usual formulation is pretty intimidating, using the jargon of "advanced" mathematical
physics. We realized that its statement
is really elementary and easy-to-understand. This does not mean that our
formulation (or rather our stronger statement) is easier-to-prove, but
it very well might. Anyway, being kind and unselfish individuals, we followed the
advice in
Dr. Z.'s Opinion 39,
and invite anyone to try to finish up our proof plan. Good luck!
.pdf
Exclusively published in the Personal Journal of Ekhad and Zeilberger
and arxiv.org
Maple Packages
Important: This article is accompanied by Maple
packages
Sample Input and Output
To verify the Razumov-Stroganov conjecture for k from 1 to 7, the
input yields the
output.
Nice pictures of Fully Packed Loops can be found in
this directory.
Added Dec. 3, 2008: Read Richard Stanley's
interesting message.
Added May 6, 2010: Luigi Cantini and Andreas Sportiello
beat us! They found a brilliant
proof.
Nevertheless, it is still possible that our suggested approach
would lead to an even nicer proof.
Doron Zeilberger's List of Papers