Enumerations of half-turn symmetric alternating-sign matrices of odd order

Details Enumerations of half-turn symmetric alternating-sign matrices of odd order Enumerations of half-turn symmetric alternating-sign matrices of odd order

2005-04-06

arxiv.org/abs/math-ph/0504022v1

Physics

Mathematical Physics

28 pages, 14 figures

Scientific paper

10.1007/s11232-006-0111-8

It was shown by Kuperberg 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 bijection with half-turn symmetric alternating-sign matrices of odd order. The partition function of the model is expressed via the above mentioned factors. The contributions to the partition function of the states corresponding to the alternating-sign matrices having 1 or -1 as the central entry are found and the related enumerations are obtained.

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