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Systems of representatives with repetition

Published online by Cambridge University Press:  24 October 2008

L. Mirsky
L. Mirsky
Affiliation:
University of Sheffield
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Extract

The part of combinatorial analysis which deals with systems of representatives draws on a variety of different sources. Thus the theory of graphs, the theory of flows in networks, linear programming, and integral linear programming all provide relevant methods and arguments. Nevertheless, it is in all likelihood possible to give a unified set-theoretic account of the subject, based in the main on Hall's criterion for the existence of transversals and on a certain generalization of the Schröder–Bernstein theorem. This approach has the added advantage of greater flexibility since it enables us sometimes to cope with transfinite situations where other methods may be only applicable to finite cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1135 - 1140
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

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