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One-transversal families
Published online by Cambridge University Press: 24 October 2008
Extract
Let I be a set and
be a family of sets Aν labelled by the elements of I. Throughout, parentheses ( ) denote families and curly brackets {} denote sets. A transversal, or system of distinct representatives, of F is, by definition, a family (xν: ν ∈ I) of objects xν, for ν ∈ I, such that †
Thus the family ({1, 2,} {1, 2}) has exactly two transversals, namely (1,2) and (2, 1). Let TF denote the set of all transversals of F. Much work has been done on the question of characterizing those F for which TF ≠ Ø. We are here going to characterize those F for which TF has exactly one element. In contrast to the more familiar case TF ≠ Ø, our argument is effective irrespective of the cardinalities of I and Aν.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 3 , May 1975 , pp. 447 - 451
- Copyright
- Copyright © Cambridge Philosophical Society 1975