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Enumeration of quarter-turn symmetric alternating-sign matrices of odd order

A. V. Razumov·Yu. G. Stroganov
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Abstract

It was shown by Kuperberg that the partition function of the square-ice model related to the 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 also written in a similar way. This allows to prove, in particular, the conjectures by Robbins related to the enumeration of the quarter-turn symmetric alternating-sign matrices.

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A. V. Razumov, Yu. G. Stroganov. 2005-07-01. Enumeration of quarter-turn symmetric alternating-sign matrices of odd order. https://doi.org/10.1007/s11232-006-0148-8

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