On refined enumerations of some symmetry classes of ASMs

Details On refined enumerations of some symmetry classes of ASMs On refined enumerations of some symmetry classes of ASMs

2003-12-29

arxiv.org/abs/math-ph/0312071v1

Theor.Math.Phys.141:1609-1630,2004; Teor.Mat.Fiz.141:323-347,2004

Physics

Mathematical Physics

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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