Geodesic
Combinatorial Nature of the Ground-State Vector of the $O(1)$ Loop Model
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 395-400

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Studying a possible connection between the ground-state vector for some special spin systems and the so-called alternating-sign matrices, we find numerical evidence that the components of the ground-state vector of the $O(1)$ loop model coincide with the numbers of the states of the so-called fully packed loop model with fixed pairing patterns. The states of the latter system are in one-to-one correspondence with alternating-sign matrices. This allows advancing the hypothesis that the components of the ground-state vector of the $O(1)$ loop model coincide with the cardinalities of the corresponding subsets of the alternating-sign matrices. In a sense, our conjecture generalizes the conjecture of Bosley and Fidkowski, which was refined by Cohn and Propp and proved by Wieland.
Keywords: loop model, ground state, fully packed loop model. 
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     author = {A. V. Razumov and Yu. G. Stroganov},
     title = {Combinatorial {Nature} of the {Ground-State} {Vector} of the $O(1)$ {Loop} {Model}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {138},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a3/}
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A. V. Razumov; Yu. G. Stroganov. Combinatorial Nature of the Ground-State Vector of the $O(1)$ Loop Model. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 395-400. http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a3/