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Catalan number

Catalan number noun: 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).

Noun

Catalan number (plural Catalan numbers)

  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.

Forms of Catalan number

pluralCatalan numbers

Origin of Catalan number

Named after the Belgian mathematician Eugène Catalan (1814–1894).

Questions about Catalan number

What does Catalan number mean?
Catalan number means 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).
What part of speech is Catalan number?
Catalan number is a noun.
What is the plural of Catalan number?
The plural of Catalan number is Catalan numbers.

Words near Catalan number in the dictionary

  1. Catalan Countries
  2. Catalan forge
  3. Catalan forges
  4. Catalan furnace
  5. Catalan Giants
  6. Catalan number
  7. Catalan numbers
  8. Catalan process
  9. Catalan Republic
  10. Catalan Sheepdog
  11. Catalan Sheepdogs

Source and license

Adapted from Wiktionary: Catalan number (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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