TOPICS

# 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 .

Bracketing, Catalan Number, Catalan's Problem

## References

Schröder, E. "Vier combinatorische Probleme." Z. Math. Physik 15, 361-376, 1870.Sloane, N. J. A. Sequence A000108/M1459 in "The On-Line Encyclopedia of Integer Sequences."Sloane, N. J. A. and Plouffe, S. Figure M1459 in The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.Stanley, R. P. "Hipparchus, Plutarch, Schröder, and Hough." Amer. Math. Monthly 104, 344-350, 1997.

## Referenced on Wolfram|Alpha

Binary Bracketing

## Cite this as:

Weisstein, Eric W. "Binary Bracketing." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BinaryBracketing.html