Geodesic
Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule
The electronic journal of combinatorics, Tome 12 (2005)

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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 $n\times n$ 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 $n\times n$ square grid with domain wall boundary conditions.
DOI : 10.37236/1903
Classification : 05A19, 82B20, 52C20 
P. Di Francesco; P. Zinn-Justin. Around the Razumov-Stroganov conjecture: proof of a multi-parameter sum rule. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1903
@article{10_37236_1903,
     author = {P. Di Francesco and P. Zinn-Justin},
     title = {Around the {Razumov-Stroganov} conjecture: proof of a multi-parameter sum rule},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1903},
     zbl = {1108.05013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1903/}
}
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