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Written: Dec. 2, 2008.

Exclusively published in the Personal Journal of Ekhad and Zeilberger
and arxiv.org

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!

## Maple Packages

Important: This article is accompanied by Maple
packages
- RS, written by Arvind Ayyer.
- FPL, written by Doron Zeilberger.

## 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
Doron Zeilberger's Home Page