2010/03/17 by Luigi Cantini, Andrea Sportiello, Cantini, Luigi +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.CO #math.MP
paper · pdf · doi:10.48550/arxiv.1003.3376
31 pages, 13 figures, typeset with elsarticle.cls
arxiv created 2010/03/17 · openalex publication_date 2010/03/17 · arxiv updated 2010/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.