Geodesic
Enumeration of quarter-turn-symmetric alternating-sign matrices of odd order
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 3, pp. 395-408

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Kuperberg showed that the partition function of the square-ice model related to quarter-turn-symmetric alternating-sign matrices of even order is the product of two similar factors. We propose a square-ice model whose states are in bijection with the quarter-turn-symmetric alternating-sign matrices of odd order and show that the partition function of this model can be written similarly. In particular, this allows proving Robbins's conjectures related to the enumeration of quarter-turn-symmetric alternating-sign matrices.
Keywords: alternating-sign matrix, enumeration, square-ice model. 
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     author = {A. V. Razumov and Yu. G. Stroganov},
     title = {Enumeration of quarter-turn-symmetric alternating-sign matrices of odd order},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {149},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_3_a6/}
}
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A. V. Razumov; Yu. G. Stroganov. Enumeration of quarter-turn-symmetric alternating-sign matrices of odd order. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 3, pp. 395-408. http://geodesic.mathdoc.fr/item/TMF_2006_149_3_a6/