Transversal (combinatorics): Difference between revisions

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Given a collection ''C'' of disjoint [[set theory|sets]], a '''transversal''' is a set containing exactly one member of each of them. In case that the original sets are not disjoint, there are several variations. One variation is that there is a [[bijection]] ''f'' from the transversal to ''C'' such that ''x'' is an element of ''f''(''x'') for each ''x'' in the transversal. Another is merely that the transversal must have non-empty intersection with each set in ''C''.

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As an example of this (disjoint-sets) meaning of ''transversal'',

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in [[group theory]], given a [[subgroup]] ''H'' of a group ''G'', a right (respectively left) transversal is a [[set]] containing exactly one element from each right (respectively left) [[coset]] of ''H''.

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== Reference ==

[[Leon Mirsky|Mirsky, Leon]] (1971).

''Transversal Theory.''

Academic Press. ISBN 0124985505.

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[[Category:Combinatorics]]

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[[Category:Group theory]]

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