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