Proof of the Razumov–Stroganov conjecture

The Razumov–Stroganov conjecture relates the ground-state coefficients in the periodic even-length dense O ( 1 ) loop model to the enumeration of fully-packed loop configurations on the square, with alternating boundary conditions, refined according to the link pattern for the boundary points. e prove this conjecture, by means 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.