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Traces of a Class Of (0, 1)-Matrices

Published online by Cambridge University Press:  20 November 2018

Dale M. Mesner*
Affiliation:
Purdue University, Lafayette, Indiana
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If A = (aij) is a matrix whose elements are 0's and l's, more briefly a (0, l)-matrix, the trace of A, defined as the sum of the diagonal elements aii and denoted by Tr A, is the number of l's on the main diagonal. Matrices which can be obtained from A by permutation of its rows or of its columns, or both, may be expressed as PA, AQ, or PAQ, respectively, where P and Q are permutation matrices.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Kônig, Denes, Théorie der endlichen und unendlichen Graphen (New York, 1950).Google Scholar
2. Ore, Oystein, Graphs and matching theorems, Duke Math. J., 22 (1955), 625639.Google Scholar
3. Ryser, H. J., Geometries and incidence matrices, Slaught Memorial Papers No. 4, Math. Assoc. Amer. (1955), pp. 25-31.Google Scholar
4. Ryser, H. J., The term rank of a matrix, Can. J. Math., 10 (1958), 5765.Google Scholar
5. Ryser, H. J., Traces of matrices of zeros and ones, Can. J. Math., 12 (1960), 463476.Google Scholar