transversaltrænsˈvɜr səl, trænz-
transversal (adj)
English Definitions:
cross(a), transverse, transversal, thwartwise (adj)
extending or lying across; in a crosswise direction; at right angles to the long axis
"cross members should be all steel"; "from the transverse hall the stairway ascends gracefully"; "transversal vibrations"; "transverse colon"
transversal (Noun)
A line which traverses or intersects any system of other lines transversely.
transversal (Noun)
A set containing one member from each of a collection of disjoint sets.
transversal (Adjective)
Running or lying across; transverse; as, a transversal line.
Transversal
In combinatorial mathematics, given a collection C of sets, a transversal is a set containing exactly one element from each member of the collection. When the sets of the collection are mutually disjoint, each element of the transversal corresponds to exactly one member of C. If the original sets are not disjoint, there are two possibilities for the definition of a transversal. One variation, the one that mimics the situation when the sets are mutually disjoint, 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. In this case, the transversal is also called a system of distinct representatives. The other, less commonly used, possibility does not require a one-to-one relation between the elements of the transversal and the sets of C. Loosely speaking, in this situation the members of the system of representatives are not necessarily distinct. A partial transversal is a set containing at most one element from each member of the collection, or a set with an injection from the set to C. The transversals of a finite collection C of finite sets form the basis sets of a matroid, the "transversal matroid" of C. The independent sets of the transversal matroid are the partial transversals of C.
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"transversal." Kamus.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.kamus.net/english/transversal>.
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