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

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

2004-10-28

arxiv.org/abs/math-ph/0410061v4

Physics

Mathematical Physics

30 pages. v2: Eq. (3.38) corrected. v3: title changed, references added. v4: q and q^{-1} switched to conform to standard conv

Scientific paper

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.

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