Geodesic
Enumerations of half-turn-symmetric alternating-sign matrices of odd order
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 3, pp. 357-386 Cet article a éte moissonné depuis la source Math-Net.Ru

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Kuperberg showed that the partition function of the square-ice model related to half-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 bijective correspondence with half-turn-symmetric alternating-sign matrices of odd order. The partition function of this model is expressed via the above factors. We find the contributions to the partition function that correspond to the alternating-sign matrices having $1$ or $-1$ as the central entry and establish the related enumerations.
Keywords: alternating-sign matrices, enumerations, square-ice model. 
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A. V. Razumov; Yu. G. Stroganov. Enumerations of half-turn-symmetric alternating-sign matrices of odd order. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 3, pp. 357-386. http://geodesic.mathdoc.fr/item/TMF_2006_148_3_a2/

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