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Remarks on Dilworth's theorem in relation to transversal theory

Published online by Cambridge University Press:  18 May 2009

Hazel Perfect
Affiliation:
University of Sheffield
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In his book Transversal Theory [3], L. Mirsky has remarked that “At present, the relation between Dilworth's decomposition theorem…and transversal theory is rather tenuous; but further study may reveal unexpected connections”. Some of these connections can perhaps now be seen a little more clearly; and our purpose in this note is to make one or two observations in this regard. Throughout, all sets considered are finite.

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Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980