On refined enumerations of some symmetry classes of ASMs

Physics – Mathematical Physics

Scientific paper

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24 pages, LaTeX2e, PSTricks package

Scientific paper

10.1023/B:TAMP.0000049757.07267.

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.

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