# Catalan numbers

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## Catalan numbers

[′kat·əl·ən ‚nəm·bərz]
(mathematics)
The numbers, cn, which count the ways to insert parentheses in a string of n terms so that their product may be unambiguously carried out by multiplying two quantities at a time.
References in periodicals archive ?
Remark 2 It is well-known (see  for instance) that involutions of length 2n without fixed points and avoiding 321 are enumerated by the n-th Catalan number.
Speakers of Catalan number about eight million, so there are enough around to get you into serious trouble.
n] is given by the nth Catalan number [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
With three words (ignoring the article "a"), the Catalan number 2 tells us we have two essentially different ways to insert parentheses.
families of mathematical objects such that the cardinality of their n-th member is given by the n-th Catalan number, defined by
The number of increasing parking functions equals the generalized Catalan number [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
It is well-known that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the n-th Catalan number, and that, for every n [greater than or equal to] 0, we have the identity:
In this case [mu](u, [upsilon]) = C([h+1/2]), the [h+1/2]-th Catalan number.
n-1] (a number famous from Cayley s formula [Cay]) and that the dimension of the sign- isotypic component is the Catalan number Cat(n, n + 1).
If we set m = 1, we get the generalized Catalan number for W.
i] is the number of parts i in [gamma], l([gamma]) is the total number of parts, and Cat(n) is the n-th Catalan number.
It is well known that noncrossing matchings of [2n] and noncrossing partitions of [n] are counted by the Catalan number [C.
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