Patterns of alternating sign matrices

  title={Patterns of alternating sign matrices},
  author={Richard A. Brualdi and Kathleen Kiernan and Seth A. Meyer and Michael W. Schroeder},
  journal={Linear Algebra and its Applications},
Abstract We initiate a study of the zero–nonzero patterns of n × n alternating sign matrices. We characterize the row (column) sum vectors of these patterns and determine their minimum term rank. In the case of connected alternating sign matrices, we find the minimum number of nonzero entries and characterize the case of equality. We also study symmetric alternating sign matrices, in particular, those with only zeros on the main diagonal. These give rise to alternating signed graphs without… Expand

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