Around the Razumov-Stroganov Conjecture: Proof of a Multi-Parameter Sum Rule

We prove that the sum of entries of the suitably normalized groundstate 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×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 × n square grid with domain wall boundary conditions.