By Arvind Ayyer and Doron Zeilberger
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
Written: Dec. 2, 2008.
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.
Doron Zeilberger's List of Papers