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

P. Di Francesco 1, Paul Zinn-Justin 2

Electronic Journal of Combinatories 12 (2005) R6

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 x 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 x n square grid with domain wall boundary conditions.

  • 1. Service de Physique Théorique (SPhT),
    CNRS : URA2306 – CEA : DSM/SPHT
  • 2. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
    CNRS : UMR7589 – Université Paris VI - Pierre et Marie Curie – Université Paris VII - Paris Diderot