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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related items

• Alternating sign matrix theorem
• Temperley-Lieb algebra

articles

• 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

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