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 Generalized Alternating Sign Matrices and Signed Permutation Matrices J. Korean Math. Soc.Published online September 18, 2020 Richard Brualdi and Hwa Kyung Kim University of Wisconsin-Madison, Sangmyung University Abstract : We continue the investigations in (R.A.~Brualdi and H.K.~Kim, A generalization of alternating sign matrices, {\it J. Combin. Des.}, 23 (2015), 204--215) extending the Bruhat order on $n\times n$ alternating sign matrices to our more general setting. We show that the resulting partially ordered set is a graded lattice with a well-defined rank function. Many illustrative examples are given. Keywords : Permutation matrix, alternating sign matrix, Bruhat order. MSC numbers : 05B20, 15B48. Full-Text :