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A generalization of Rado's theorem on independent transversals

Published online by Cambridge University Press:  24 October 2008

Hazel Perfect
Hazel Perfect
Affiliation:
University of Sheffield
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Extract

The growth of transversal theory has been greatly enriched by the study of abstract independence. In this development, Rado's theorem on independent transversals (4) has played a prominent role, and recent work (e.g. by Welsh(7)) suggests that its applications are by no means exhausted. Rado's theorem can be extended in many directions, and my object is to describe a further generalization (Theorem 2 below) which does not seem to have been noted in the literature.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 3 , November 1969 , pp. 513 - 515
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Hall, M. Jr. Distinct representatives of subsets. Bull. Amer. Math. Soc. (1948), 922–926.CrossRefGoogle Scholar
(2)Hall, P.On representatives of subsets. J. London Math. Soc. 10 (1935), 26–30.CrossRefGoogle Scholar
(3)Mirsky, L. A proof of Rado's theorem on independent transversals. Unpublished.Google Scholar
(4)Rado, R.A theorem on independence relations. Quart. J. Math. Oxford Ser. 13 (1942), 83–89.CrossRefGoogle Scholar
(5)Rado, R.Axiomatic treatment of rank in infinite sets. Canad. J. Math. 1 (1949), 337–343.CrossRefGoogle Scholar
(6)Rado, R.Abstract linear dependence. Colloq. Math. 14 (1966), 257–264.CrossRefGoogle Scholar
(7)Welsh, D. J. A.Some applications of a theorem of Rado. Mathematika 15 (1968), 199–203.CrossRefGoogle Scholar
(8)Whitney, H.On the abstract properties of linear dependence. Amer. J. Math. 57 (1935), 509–533.CrossRefGoogle Scholar