关于有限集[n]及其子集若干性质的讨论  

Discussion on the Nature of the Finite Set [n] and Its Subsets

作　　者：程杰[1] 杨冬苹 

机构地区：[1]重庆师范大学数学学院,重庆401331 [2]重庆市秀山高级中学,重庆409900

出　　处：《重庆工商大学学报（自然科学版）》2015年第5期52-54,共3页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市自然科学基金(2011jj A00003)

摘　　要：有限集由于有有限多个子集,因而具有许多无限集合所不具有的性质;从n元有限集的所有k元子集元素和入手,得到了n元有限集的全体子集元素和Sn的计数公式,以及所有k阶子集的元素和Sn,k(k=0,1,2,…,n)的计数公式以及单峰性质和其他一些推论.Because finite set contains limited subsets, it has many properties infinite set doesn＇ t have. This paper begins with the sum of all elements of subsets with k elements in finite set with n elements, gains calculating formula for Sn, the sum of all elements of subsets in finite set with n elements, and gets calculating formula for Sn.k （k = 0,1,2,…, n） , the sum of all elements of subsets with k order as well as unimodal nature and some other inferences.

关 键 词：计数公式 有限集 有限子集 二项式系数 

分 类 号：O175[理学—数学]