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所谓计数,就是估计或计算符合某些要求的对象的个数,换言之,就是给定-个有限集合S,要求出集合S所含的元素的个数|S|,或者对集合S的阶的上、下界进行估计.由于通常给定的集合各种各样,要判定一个元素是否属于它,绝非易事,要计算它所含元素的个数就更加困难.所以,如何计数的问题长期以来一直是人们关心的问题,它历来是组合数学研究的基本课题之一,也是各类竞赛的热点之一.
The so-called counting, is to estimate or calculate the number of objects that meet certain requirements, in other words, is to give a finite set S, requires the number of elements contained in the set S | S |, or the order of the set S The upper and lower bounds are estimated. Since usually a given set is varied, it is not easy to determine whether an element belongs to it. It is more difficult to calculate the number of elements it contains. So, how to count the long-term problem Has always been a concern of people, it has always been one of the basic topics of combinatorial mathematics research, but also one of the hot spots of various competitions.