On refined enumerations of some symmetry classes of ASMs

A. V. Razumov, Yu. G. Stroganov

Published 2003-12-29Version 1

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.