Symmetric alternating sign matrices
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In this note we consider completions of n×n symmetric (0,−1)-matrices to symmetric alternating sign matrices by replacing certain 0s with +1s. In particular, we prove that any n×n symmetric (0,−1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with +1s can be completed to a symmetric alternating sign matrix. Similarly, any n × n symmetric (0,+1)-matrix that can be completed to an alternating sign matrix by replacing some 0s with −1s can be completed to a symmetric alternating sign matrix.
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[2] Richard A. Brualdi,et al. Patterns of alternating sign matrices , 2011, 1104.4075.