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| Fourteen ways of triangulating a hexagon Image credit: User:Dmharvey |
The Catalan numbers, named for the Belgian mathematician Eugène Charles Catalan, are a sequence of natural numbers that are important in combinatorial mathematics. The sequence begins:
The Catalan numbers are solutions to numerous counting problems which often have a recursive flavour. In fact, one author lists over 60 different possible interpretations of these numbers. For example, the nth Catalan number is the number of full binary trees with n internal nodes, or n+1 leaves. It is also the number of ways of associating n applications of a binary operator as well as the number of ways that a convex polygon with n + 2 sides can be cut into triangles by connecting vertices with straight lines. (Full article...)
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