  The Razumov-Stroganov conjecture relates the ground-state coefficients in the
even-length dense O(1) loop model to the enumeration of fully-packed loop
configuration on the square, with alternating boundary conditions, refined
according to the link pattern for the boundary points. Here we prove this
conjecture, by mean of purely combinatorial methods. The main ingredient is a
generalization of the Wieland proof technique for the dihedral symmetry of
these classes, based on the `gyration' operation, whose full strength we will
investigate in a companion paper.
