[1]吴建东,杨全会.和集与给定序列相交问题[J].南京师范大学学报(自然科学版),2012,35(02):22-23.
 Wu Jiandong,Yang Quanhui.Sumsets Intersecting a Sequence[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(02):22-23.
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和集与给定序列相交问题()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第35卷
期数:
2012年02期
页码:
22-23
栏目:
数学
出版日期:
2012-06-20

文章信息/Info

Title:
Sumsets Intersecting a Sequence
作者:
吴建东;杨全会;
南京师范大学数学科学学院、数学研究所,江苏南京210046
Author(s):
Wu JiandongYang Quanhui
School of Mathematical Sciences and Institute of Mathematics,Nanjing Normal University,Nanjing 210046,China
关键词:
和集序列
Keywords:
sumsetssequences
分类号:
O156
摘要:
设{an}∞n=1是无界的正整数序列,满足当n→∞时an+1/an→α.设β>max{α,2}.则存在x0,对所有x>x0,若A,B是[0,x]的子集且满足0∈A∩B,|A|+|B|≥2 (1-1/β)x,则和集A+B包含序列{an}的元素.本文是Kapoor V结果的一般化.
Abstract:
Let { an } ∞ n = 1 be an unbounded sequence of positive integers with an + 1 /an→α as n→∞,and let β > max{ α, 2} . Then there exists an x0 such that for all x > x0 and if A,B[0,x] are sets of nonnegative integers with 0∈A∩B and | A| + | B|≥2(1 - 1 ) β x, then the sumset A + B contains an element of the sequence { an } . This generalizes a recent result by Kapoor V.

参考文献/References:

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[3] Nathanson M B,Srkzy A. Sumsets containing long arithmetic progressions and powers of 2[J]. Acta Arith,1989( 54) : 147-154.
[4] Lev V F. Representing powers of 2 by a sum of four integers[J]. Combinatorica,1996( 16) : 413-416.
[5] Pan Hao. Note on integer powers in sumsets[J]. J Number Theory,2006( 117) : 216-221.
[6] Abe T. Sumsets containing powers of an integer[J]. Combinatorica,2004( 24) : 1-4.
[7] Alon N. Subset sums[J]. J Number Theory,1987( 27) : 196-205.
[8] Nathanson M B. Additive Number Theory: Inverse Problems and the Geometry of Sumsets. Volume 165 of Graduate Texts in Mathematics[M]. New York: Springer-Verlag,1996.
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备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 11071121) 、江苏省研究生科研创新计划项目( CXLX11 - 0862) .
通讯联系人: 吴建东,博士,讲师,研究方向: 数论. E-mail: wjd. njnu@163. com
更新日期/Last Update: 2013-03-11