Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T00:59:46.268Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Gale, David, A theorem onflows in networks, Pacific J. Math., 7 (1957), 1073-1082.Google Scholar
2. Hall, P., On representatives of subsets, J. Lond. Math. Soc, 10 (1935), 26-30.Google Scholar
3. König, Dénes, Théorie der endlichen und unendlichen Graphen (New York, 1950).Google Scholar
4. Ore, Oystein, Graphs and matching theorems, Duke Math. J., 22 (1955), 625-639.Google Scholar
5. Ryser, H. J., Combinatorial properties of matrices of zeros and ones, Can. J. Math., 9 (1957), 371-377.Google Scholar