Geodesic
Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns
The electronic journal of combinatorics, Tome 13 (2006)
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We prove the Razumov–Stroganov conjecture relating ground state of the $O(1)$ loop model and counting of Fully Packed Loops in the case of certain types of link patterns. The main focus is on link patterns with three series of nested arches, for which we use as key ingredient of the proof a generalization of the MacMahon formula for the number of plane partitions which includes three series of parameters.
DOI : 10.37236/1136
Classification : 82B23, 82B20, 05A19 
@article{10_37236_1136,
     author = {P. Zinn-Justin},
     title = {Proof of the {Razumov-Stroganov} conjecture for some infinite families of link patterns},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1136},
     zbl = {1119.82018},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1136/}
}
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P. Zinn-Justin. Proof of the Razumov-Stroganov conjecture for some infinite families of link patterns. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1136

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