Transversal (combinatorics): Difference between revisions

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Revision as of 20:17, 9 October 2005

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As an example of the first (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''.

[[Image:Parallel_lines.png|thumb|right|300px250px|A transversal cutting two parallel lines]]

A transversal in a [[Latin square]] of order ''n'' is a collection of ''n'' matrix positions comprising one from each row and one from each column, such that the symbols in those positions are distinct. Not all Latin squares have transversals.

[[Image:Parallel_lines.png|thumb|right|300px|A transversal cutting two parallel lines]]

In [[geometry]], a '''transversal''' is a line that intersects two or more [[parallel lines]]. Such a line produces several [[congruent]] and several [[supplementary angles]].

== Reference ==

* [[Leon Mirsky|Mirsky, Leon]] (1971).
''Transversal Theory.''
Academic Press. ISBN 0124985505.

==External==

* [http://www.gmi.edu/~drussell/Demos/waves/wavemotion.html Animation of a Transverse Wave Motion]

* [http://hyperphysics.phy-astr.gsu.edu/hbase/sound/tralon.html Transverse Wave example]

[[Category:Combinatorics]]