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关于极小论文范文资料 与关于C8⊕C8中极小零和子列一个性质有关论文参考文献

版权:原创标记原创 主题:极小范文 科目:论文范文 2024-03-17

《关于C8⊕C8中极小零和子列一个性质》:本文关于极小论文范文,可以做为相关论文参考文献,与写作提纲思路参考。

摘 要:如果在群CnCn中,每个含有2n-1个元素的极小零和序列中都包含一些阶数为n-1的元素,那么我们称正整数n具有性质B.在二维阿贝尔群的零和理论中,性质B是一个中心议题.关于性质B这一问题最早是由高维东教授和A.Geroldinger提出并进行研究[1-3].之后,他们证明了如果n具有性质B[4-6],当n大于等于6时,2n也具有性质;还证明了如果n∈{2,3,4,5,6,7},n具有性质B.在文[7]中,我们证明了n等于10时,n具有性质B.本文证明n等于8时,n也具有性质B.

关键词:阿贝尔群;零和子列;性质B

DOI:10.15938/j.jhust.2017.06.021

中图分类号: O156.1

文献标志码: A

文章编号: 1007-2683(2017)06-0113-03

Abstract:We say a positive integer n has Property B if every minimal zerosum subsequence of 2n-1 elements in CnCn contains some elements n-1 times. Property B is a central topic in zerosum theory on abelian group G with rank two. Property B has been first formulated and investigated by professer W.D.Gao and A.Geroldinger in [1-3]. It has been proved that if n≥6 and if n has Property B, then 2n has Property B. It has been also proved that if n∈{2,3,4,5,6,7}, then n has property B[4-6]. In [7], we proved that n等于10 has Property B. In this paper, we will verify that n等于8 has Property B.

Keywords:abelian group; zerosum subsequence; Property B

Similar to the proof of case 1, we can verify that there are at most two distinct elements in Tof case2 and case 3.

Theorem is true.

References:

[1] GAO W D, GEROLDINGER A. On Long Minimal Zero Sequences in Finite Abelian Groups[J]. Period Math. Hungar, 1999(38):179-211.

[2] GAO W D, GEROLDINGER A. On Zerosum Sequences in Z/nZ Z/nZ[J]. Integers, 2003(3) (Paper A08).

[3] GAO W D, ZHUANG J J. Sequences not Containing Long Zerosum Subsequences[J]. European J. Combin, 2006(27): 777-787.

[4] GAO W D, GEROLDINGER A. Zerosum Probiems in Finite Abelian Groups: a survey[J]. Expo.Math, 2006(24): 337-369.

[5] CHANG G J, CHEN S H, WANG G Q, et al. On the Number of Subsequences with a Given Sum in a Finite Abelian Group[J]. Electron. J. Combin, 2011(18): 133-157.

[6] CHINTAMANI M N, MORIYA B K, GAO W D, et al. New Upper Bounds for the Davenport and for the ErdosGinzburgZiv Constants[J]. Arch. Math., 2012(98):133-142.

[7] ZANG H Y, LIU W H. A Property on Minimal Zerosum Subsequence inC10C10[J]. Advanced Materials Research ICEEIS2016981,2014:255-257.

[8] 韓冬春. ErdosGinzburgZiv Theorem for Finite Nilpotent Groups[J]. Arch. Math, 2015(104): 325-332.

[9] GAO W D,LI Y L, YUAN P Z,et al. On the Structure of Long Zerosum Free Sequences and Nzerosum Free Sequences Over Finite Cyclic Groups[J]. Arch. Math, 2015(105): 361-370.

[10]高维东,韩冬春,PENG J T, et al. On Zerosum Subsequences of Length k*exp(G)[J]. J. Combin. Theory Ser. 2014(A125):240-253.

[11]ADHIKARIA S D,高维东,WANG G Q. ErdosGinzburgZiv Theorem for Finite Commutative Semigroups[J]. J. Pure Appl. Algebra, 2014(218):1838-1844.

[12]高维东,路在平. The ErdsGinzburgZiv Theorem for Dihedral Groups[J]. J. Pure Appl. Algebra, 2008(212): 311-319.

[13]高维东,侯庆虎,SCHMID W, et al. On Short Zerosum Subsequences II[J]. Integers,2007(7):21-56.

[14]GAO W D, Alfred Geroldinger. On a Property of Minimal Zerosum Sequences and Restricted Sumsets[J]. Bull. London Math. Soc, 2005(37):321-334.

[15]高维东,PENG J T,钟庆海. A Quantitative Aspect of Nonunique Factorizations: the Narkiewicz Constants III[J]. Acta Arith., 2013(158):271-285.

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极小论文参考资料:

科技小发明论文

大学生小论文范文

小论文排版与格式

初中历史小论文范文

科技小论文500字

小论文查重

结论:关于C8⊕C8中极小零和子列一个性质为关于本文可作为相关专业极小论文写作研究的大学硕士与本科毕业论文第一级极小论文开题报告范文和职称论文参考文献资料。

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