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Combinatorial Properties of Matrices of Zeros and Ones

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 is concerned with 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 (i = 1, … , m) and let the sum of column i of A be denoted by si (i = 1, … , n).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 371 - 377
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Hall, Marshall, An existence theorem for Latin squares, Bull. Amer. Math. Soc, 51 (1945), 387–388.Google Scholar
2. Hall, P., On representatives of subsets, J. Lond. Math. Soc, 10 (1935), 26–30.Google Scholar
3. Hardy, G. H., Littlewood, J. E., and Pólya, G., Inequalities (Cambridge, 1952).Google Scholar
4. König, Dénes, Theorie der endlichen und unendlichen Graphen (New York, 1950).Google Scholar
5. Muirhead, R. F., Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters, Proc. Edinburgh Math. Soc, 21 (1903), 144–157.Google Scholar
6. Ore, Oystein, Graphs and matching theorems, Duke Math. J., 22 (1955), 625–639.Google Scholar
7. Ryser, H. J., A combinatorial theorem with an application to Latin rectangles, Proc. Amer. Math. Soc, 2 (1951), 550–552.Google Scholar