Catalan数的一个递归关系

A new recurrence relation of the catalan number

将非结合代数中n元X1 ,X2 ,… ,Xn 按给定次序的加括号乘法 (结合法 )转化为长为n- 1的路X1 X2 …Xn 的边收缩问题 ,用容斥原理 。

By setting up a bijection between the problem of putting brackets in the product of n elements X 1,X 2,…,X n in a non associative algebra and that of edges contraction of the path X 1X 2…X n ,a new recurrence relation related to the catalan number is obtained.