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

P. Di Francesco·P. Zinn-Justin
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Abstract

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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P. Di Francesco, P. Zinn-Justin. 2006-03-07. Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule. https://arxiv.org/abs/math-ph/0410061

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