Two problems on subset sums

IF 1 3区 数学 Q1 MATHEMATICS
Xing-Wang Jiang , Bing-Ling Wu
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引用次数: 0

Abstract

For a set A of positive integers, let P(A) denote the set of all finite subset sums of A. In this paper, we completely solve a problem of Chen and Wu by proving that if B={b1<b2<} is a sequence of integers with b111, 3b1+5b24b1, 3b2+2b33b2+b1 and 3bnbn2bn+13bn(n3), then there exists a set of positive integers A for which P(A)=NB. We also partially answer a problem of Wu by determining the structure of B={b1<b2<} with b1>10 and b2>3b1+4, for which there exists a set of positive integers A such that P(A[0,bk])=[0,2bk]{bi,2bkbi:1ik}(k2).

关于子集和的两个问题
对于正整数集合 A,让 P(A) 表示 A 的所有有限子集和的集合。本文通过证明如果 B={b1<b2<⋯} 是一个具有 b1≥11,3b1+5≤b2≤4b1,3b2+2≤b3≤3b2+b1 和 3bn-bn-2≤bn+1≤3bn(n≥3)的整数序列,完全解决了陈和吴的一个问题,那么存在一个正整数集 A,对于它,P(A)=N∖B。我们还通过确定 B={b1<b2<⋯} 的结构(b1>10 和 b2>3b1+4)部分地回答了吴的一个问题,即存在一组正整数 A,使得 P(A∩[0,bk])=[0,2bk]∖{bi,2bk-bi:1≤i≤k}(k≥2)。
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来源期刊
CiteScore
2.10
自引率
10.00%
发文量
124
审稿时长
4-8 weeks
期刊介绍: The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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