Transversal (combinatorics)

For other uses, see Transversal (combinatorics) (disambiguation).

Given a collection C of disjoint 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.

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

Reference

• Mirsky, Leon (1971). Transversal Theory. Academic Press. ISBN 0124985505.