Catalan number
nounEtymology Named after the Belgian mathematician Eugène Catalan (1814–1894).
1
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).
- 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 number1998 July 29, Michael Collins, “A CONTEXT-FREE GRAMMAR FOR ENGLISH”, in http://old-site.clsp.jhu.edu/ws98/projects/nlp/, retrieved 19 Apr 2013:
- 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.