File:Noncrossing_partitions_5.svg · Wikimedia Commons · See Wikimedia Commons
Wikidata facts
- Image
- Catalan 4 leaves binary tree example.svg
Show 2 more facts
- time of discovery or invention
- 1800-00-00
- Commons category
- Catalan numbers
via Wikidata · CC0
~30 min read
Article
The C5 = 42 noncrossing partitions of a 5-element set (below, the other 10 of the 52 partitions) The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after Eugène Catalan, though they were previously discovered in the 1730s by Minggatu.
The n-th Catalan number can be expressed directly in terms of the central binomial coefficients by
Gallery (12)
Connections
prime number
Entity
figurate number
Entity
automorphic number
Entity
double Mersenne number
Entity
Minggatu
Entity
Bertrand's ballot theorem
Entity
Dyck language
Entity
China
Country
Leonhard Euler
Entity
triangle
Entity
International Standard Book Number
Entity
natural number
Entity
integer
Entity
digital object identifier
Entity
binary numeral system
Entity
digit
Entity
exponentiation
Entity
quadratic equation
Entity
numeral system
Entity
combinatorics
Entity