Catalan number
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English
Etymology
Named after the Belgian mathematician Eugène Catalan (1814–1894).
Noun
Catalan number (plural Catalan numbers)
- In combinatorial mathematics, any of a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects; the nth Catalan number is equal to (2n choose n) over (n+1).
- 1998 July 29, Michael Collins, “A CONTEXT-FREE GRAMMAR FOR ENGLISH”, in http://old-site.clsp.jhu.edu/ws98/projects/nlp/, retrieved 2013-04-19:
- AMBIGUITY LEADS TO AN EXPONENTIAL NUMBER OF TREES
I saw the man with the telescope on the box in the car under the table ...
n prepositional phrases ⇒ (n + 1)’th catalan number
- Cn — the nth Catalan number — could be described as the number of distinct ways in which a sequence of n + 1 numbers could be associated by means of some specified binary operator.