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The Term Rank of a Matrix

Published online by Cambridge University Press:  20 November 2018

H. J. Ryser
H. J. Ryser*
Affiliation:
Ohio State University
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This paper continues a study appearing in (5) of the combinatorial properties of a matrix A of m rows and n columns, all of whose entries are 0's and 1's. Let the sum of row i of A be denoted by ri and let the sum of column i of A be noted by st. We call R = (r1, … , rm) the row sum vector and S = (s1, … , sn) the column sum vector of A. The vectors R and S determine a class consisting of all (0, 1)-matrices of m rows and n columns, with row sum vector R and column sum vector S. Simple arithmetic properties of R and S are necessary and sufficient for the existence of a class (1 ; 5).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 57 - 65
Copyright
Copyright © Canadian Mathematical Society 1958

References

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