Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule (Q1773196)

We prove that the sum of entries of the suitably normalized ground-state vector of the \(O(1)\) loop model with periodic boundary conditions on a periodic strip of size \(2n\) is equal to the total number of \(n\times n\) alternating sign matrices. This is done by identifying the state sum of a multi-parameter inhomogeneous version of the \(O(1)\) model with the partition function of the inhomogeneous six-vertex model on a \(n\times n\) square grid with domain wall boundary conditions.