  Using determinant representations for partition functions of the
corresponding square ice models and the method proposed recently by one of the
authors, we investigate refined enumerations of vertically symmetric
alternating-sign matrices, off-diagonally symmetric alternating-sign matrices
and alternating-sign matrices with U-turn boundary. For all these cases the
explicit formulas for refined enumerations are found. It particular, Kutin-Yuen
conjecture is proved.
