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Combinatorial class
In combinatorics, a combinatorial class (or simply class) is an equivalence class of sets that have the same counting sequence. Although the elements of these equivalent sets may have very different definitions and semantics, combinatorics is concerned only with the number of elements of a given size. Therefore, knowledge about one set in the class can be applied directly to other sets in the class.
For example, the set of triangulations of polygons is combinatorially isomorphic to the set of general rooted plane trees. Although these sets certainly describe different things, they have the same counting sequence, namely the Catalan numbers.
See also: double counting, combinatorial species.
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details