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Essential coverings of matrices

Published online by Cambridge University Press:  24 October 2008

M. Lewin
M. Lewin
Affiliation:
University of Reading†.
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Extract

Let G be a matrix. If there does not exist an infinite set of non-zero elements such that no two are on the same line (row or column), the matrix is said to be of finite term-rank. A set of lines such that each non-zero element belongs to some line of the set is said to be a covering of G.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 263 - 267
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)König, D.Über trennende Knotenpunkte in Graphen. Acta Lit. Sci. Sect. Sci. Math., Szeged 6 (1933), 155–179.Google Scholar
(2)Lewin, M. An extension of König's theorem to infinite bipartite graphs. Not yet published.Google Scholar
(3)Mursky, L. and Perfect, H.Systems of representatives. J. Math. Anal. Appl. 15 (1966), 520–568.CrossRefGoogle Scholar
(4)Mirsky, L. and Perfect, H.Applications of the notion of independence to problems of combinatorial analysis. J. Combinatorial Theory 2, (1967), 327–357.Google Scholar
(5)Rado, R.Axiomatic treatment of rank in infinite sets. (Janad. J. Math. 1 (1949), 337–343.Google Scholar
(6)Whitney, H.On the abstract properties of linear dependence. Amer. J. Math. 57 (1935), 509–533.Google Scholar