###### Mathematics

## Grouping with Parentheses and Catalan Numbers

Problem Suppose we have \( n \) numbers \(x_{1},x_{2}, \cdots x_{n} \), in that order. Compute the number \(C_{n} \) of ways of positioning the brackets to multiply the product of the \(n\) numbers, without changing the given order. HintIf \(n=2\) we have only one case: \((x_{1} x_{2})\) If \(n=3\) Read more…