A Generalization of Alternating Sign Matrices
Copyright policy )A Generalization of Alternating Sign Matrices
AbstractIn alternating sign matrices, the first and last nonzero entry in each row and column is specified to be +1. Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry in each row and column to be either a +1 or a −1. We determine necessary and sufficient conditions for such matrices to exist whose proof contains an algorithm for their construction.
- University of Wisconsin–Madison United States
- Sangmyung University Korea (Republic of)
- University of Wisconsin–Oshkosh United States
Graphs and linear algebra (matrices, eigenvalues, etc.), alternating sign matrix (ASM), square-ice configuration, Matrices of integers, Signed and weighted graphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05B20, 05C22, 05C50, 15B35, 15B36, Sign pattern matrices, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
Graphs and linear algebra (matrices, eigenvalues, etc.), alternating sign matrix (ASM), square-ice configuration, Matrices of integers, Signed and weighted graphs, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), 05B20, 05C22, 05C50, 15B35, 15B36, Sign pattern matrices, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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