某些数集的秩的下界(英文)  

Lower Bounds on the Ranks of Some Sets of Numbers

作　　者：郭曙光[1] 

机构地区：[1]南京师范大学数学与计算机科学学院

出　　处：《南京师大学报（自然科学版）》2003年第2期1-5,共5页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：SupportedbytheNationalNaturalScienceFoundationofChina(10 2 0 10 13) .

摘　　要：　设B为有限实数集,称{ a∈AaA B}为B的张成集,记为sp(B).对于一个有限实数集P,称满足P sp(B)的集合B的最小基数为P的秩,记为rk(P).本文给出rk(sp(A)),rk(1,r,…,rn-1)和rk(1,a1,a1a2,…,a1a2…an-1)的下界,其中A为有限实数集,r为不等于1的正有理数,a1,a2,…,an-1为大于1的整数.The span sp(B) of a finite set Bof real numbers is defined to be the set {a∈AaAB}. The rank of a set P of real numbers,denoted by rk(P),is the smallest size of a set B with Psp(B). In this paper,we provide a lower bound on the rank of sp(A) for any finite set Aof real numbers and the lower bounds of rk(1,r,...,rn-1) and rk(1,a1,a1a2,...,a1a2...an-1),where r is an arbitrary positive rational number different from 1 and ai(i=1,...,n-1) are n-1 arbitrary integers greater than 1.

关 键 词：有限实数集 最小基数 数集 秩 下界 张成集 数论 子集和 

分 类 号：O156.1[理学—数学]