Abstract
Using determinant representations for partition functions of the corresponding variants of square-ice models and the method recently proposed by one of us, we investigate refined enumerations of vertically symmetric alternating-sign matrices, off-diagonally symmetric alternating-sign matrices, and alternating-sign matrices with a U-turn boundary. For all these cases, we find explicit formulas for refined enumerations. In particular, we prove the Kutin–Yuen conjecture.
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