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Traces of Matrices of Zeros and Ones

Published online by Cambridge University Press:  20 November 2018

H. J. Ryser
H. J. Ryser*
Affiliation:
The Ohio State University
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This paper continues the study appearing in (9) and (10) of the combinatorial properties of a matrix A of m rows and n columns, all of whose entries are 0's and l's. Let the sum of row i of A be denoted by ri and let the sum of column j of A be denoted by Sj. 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

1.1

consisting of all (0, 1)-matrices of m rows and n columns, with row sum vector R and column sum vector S. The majorization concept yields simple necessary and sufficient conditions on R and S in order that the class 21 be non-empty (4; 9). Generalizations of this result and a critical survey of a wide variety of related problems are available in (6).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 463 - 476
Copyright
Copyright © Canadian Mathematical Society 1960

References

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