正确排列括号的方法数
Number of ways of correctly arranging parenthesis
这个问题我想了很久：
What's the number of ways of correctly* arranging 2*n parenthesis.
*A correctly arranged sequence of parenthesis has an equal number of open and closed parenthesis at its end and a larger or equal amount of open parenthesis than the closed ones throughout the sequence.
例如n=3，有5种方式：((())), ()(()), ()()(), (())(), (()()).
我一直在考虑将嵌套括号表示为树，但没有取得太大进展。
你的例子相当于Dyck words, which can be counted with combinatorics and will be equal to Catalan number的数量：
这个问题我想了很久：
What's the number of ways of correctly* arranging 2*n parenthesis.
*A correctly arranged sequence of parenthesis has an equal number of open and closed parenthesis at its end and a larger or equal amount of open parenthesis than the closed ones throughout the sequence.
例如n=3，有5种方式：((())), ()(()), ()()(), (())(), (()()).
我一直在考虑将嵌套括号表示为树，但没有取得太大进展。
你的例子相当于Dyck words, which can be counted with combinatorics and will be equal to Catalan number的数量：