关于排列组合的一个问题

A Certain Problem about Permutation and Combination

本文是证明排列组合的一个证明Cn2n-Cn+12n=Cn2n/n+1。作者把数列的排序抽象成表格中的上下问题,再把上下赋值为-1和1,建立坐标系,将数字0,1,2,……,2n作横坐标,对应数字前的所有箭头上数字之和为纵坐标,从而将升降抽象成坐标中的折线,最终证明Cn2n-Cn+12n=Cn2n/n+1。

This paper is to demonstrate a proof of permutations and combinations Cn2n-Cn＋12n=Cn2n/n＋1.The writer abstracts the sequence into the problem up and down with respect to the form,then makes evaluation of -1 and 1 from up to down,then establishes coordinate system with the number 0,1,2,......,2n for the abscissa and the corresponding number on the front of all the arrows figures for the vertical axis,which abstracts up-down movement into the line in a coordinate system.Eventually,the equation is proved,that is,Cn2n-Cn＋12n=Cn2n/n＋1.