Proof of Razumov-Stroganov conjecture for some infinite families of link patterns

Abstract

We prove the Razumov--Stroganov conjecture relating ground state of the O(1) loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches, for which we use as key ingredient of the proof a generalization of the Mac Mahon formula for the number of plane partitions which includes three series of parameters.

References in corpus (6)

• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• Combinatorial nature of ground state vector of O(1) loop model
• Quantum Knizhnik-Zamolodchikov equation, generalized Razumov-Stroganov sum rules and extended Joseph polynomials
• Temperley-Lieb Stochastic Processes
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Loops, matchings and alternating-sign matrices

Cited by in corpus (3)

• Six-Vertex, Loop and Tiling models: Integrability and Combinatorics
• Grassmann-Grassmann conormal varieties, integrability, and plane partitions
• A bijectional attack on the Razumov-Stroganov conjecture