Binary Bracketing
A binary bracketing is a bracketing built up entirely of binary operations. The number of binary bracketings
of 
letters (Catalan's
problem) are given by the Catalan numbers 
, where
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
denotes a binomial
coefficient and 
is the usual factorial,
as first shown by Catalan in 1838. For example, for the four letters 
, 
, 
, and 
there are five
possibilities: 
, 
, 
, 
, and 
, written in shorthand as 
, 
, 
, 
, and 
.
Contact the MathWorld Team
11th Boolean function of 2 variables
