Razumov-Stroganov Conjecture

introduction

The Razumov-Stroganov correspondence, an important link between statistical physics and combinatorics proved in 2011 by L. Cantini and A. Sportiello
- the ground-state coefficients in the even-length dense O(1) loop model
- the enumeration of fully-packed loop configuration on the square, with alternating boundary conditions, refined according to the link pattern for the boundary points
relates the ground state eigenvector of the O(1) dense loop model on a semi-infinite cylinder to a refined enumeration of fully-packed loops, which are in bijection with alternating sign matrices.
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Striker, Jessica. ‘The Toggle Group, Homomesy, and the Razumov-Stroganov Correspondence’. arXiv:1503.08898 [cond-Mat, Physics:math-Ph], 30 March 2015. http://arxiv.org/abs/1503.08898.
Cantini, Luigi, and Andrea Sportiello. ‘Proof of the Razumov-Stroganov Conjecture’. arXiv:1003.3376 [cond-Mat, Physics:math-Ph], 17 March 2010. http://arxiv.org/abs/1003.3376.
Around the Razumov–Stroganov conjecture: proof of a multi-parameter sum rule