关于有限数列的一个问题的注记  

On the Problem of a Finite Sequence of Positive Integers

作　　者：孙茂荣[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2002年第5期31-33,共3页Journal of Jiangsu University：Natural Science Edition

摘　　要：为了揭示有限数列的某些性质 ,利用抽屉原理对下面问题进行讨论 ,设x1,x2 ,… ,xn,y1,y2 ,… ,yk2 ∈ { 1,2 ,… ,k} ,并且x1+x2 +… +xn ≥ y1+ y2 +… + yk2 ,则存在≠I { 1,2 ,… ,n} ,≠J { 1,2 ,… ,k2 } ,使 i∈Ixi = j∈Jyi,得出一些结果 主要结果有在零点附近符合某些条件的有限整数数列 ,必存在子数列 ,它的和为零 ;在零点附近都大于零而且符合某些条件的有限整数数列 ,必存在两个子数列 。Pigeon hole principle is used in discussing following question in order to reveal some characters of finite sequence. If x 1,x 2,...,x n,y 1,y 2,...,y k 2 ∈{1,2,...,k} , and x 1+x 2+...+x n≥y 1+y 2+...y k 2 , then there exist ≠I{1,2,...,n} and ≠J{1,2,...,k 2} such that  i∈I x i= j∈J y i, followed by some results. The main results are: if the finite integer's sequence accords with some terms near zero point, there must have a subsequence, and their sum must be zero; if the finite sequence is greater than zero and accords with some terms near zero point, there should have two subsequences, and their sum are equal.

关 键 词：有限数列 抽屉原理 指标集 有限整数数列 零点 数学归纳法 

分 类 号：O156.1[理学—数学]