Proof of the Razumov-Stroganov conjecture

Details Proof of the Razumov-Stroganov conjecture Proof of the Razumov-Stroganov conjecture

2010-03-17

arxiv.org/abs/1003.3376v1

Mathematics

Combinatorics

31 pages, 13 figures, typeset with elsarticle.cls

Scientific paper

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.

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