Catalan numbers

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 ?
The sequence of Catalan numbers begins (1, 2, 5, 14, 42, .
n-1], these reduce to objects counted by the classical Catalan numbers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], namely the set of noncrossing partitions of [n] = {1, 2, .
This text has been developed out of a minicourse given by Grimaldi (mathematics, Rose-Hulman Institute of Technology) at national mathematics meetings on examples, properties, and applications of the sequences of the Fibonacci and Catalan numbers.
4] Liu Jianjun, Ming Antu and Catalan Numbers, Journal of Mathematical Research and Exposition, 22(2002), 589-594.
Discover the properties and real-world applications of the Fibonacci and the Catalan numbers
Loehr, Multivariate analogues of Catalan numbers, parking functions, and their extensions.
5] WangFengxiao and Fu Li, Several different solutions to Catalan Numbers, Journal of Shaanxi Institute of Technology, 16(2000), 78-81.
10, 11], related the combinatorics of Catalan numbers and parking functions to the space of diagonal harmonics.
For any positive integer n, the classical Catalan numbers [b.
It is well known that Catalan numbers [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] enumerate many combinatorial objects, such as binary trees and parallelogram polyominoes.
Our results show that all such polynomials have nonnegative coefficients, conjectured by Kazhdan and Lusztig (1979), and give a combinatorial interpretation of them in terms of Catalan numbers and the Coxeter graph of the group.
is the well known Carlitz q-analogue of Catalan numbers.