初等3-群中表出达文波特常数的极小集  

Representation of the Minimal Set of Davenport Constants in the Elementary 3-group

作　　者：赵小越 吴雄华[1] Zhao Xiaoyue;Wu Xionghua(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《洛阳师范学院学报》2023年第11期1-4,共4页Journal of Luoyang Normal University

摘　　要：令G是一个有限阿贝尔群,群G上的所有零和序列构成的幺半群记为B(G),Ω是B(G)上的一个子集,定义dΩ(G)是一个最小的整数t使得G上每个长度大于等于t的序列S都在Ω上有子序列.对于d_(Ω)(G)=t≥D(G)的Ω被称为d_(Ω)(G)=t的最小Ω,如果Ω的每个真子集Ω1都有d_(Ω1)(G)>t.dΩ(G)=D(G)的最小Ω被称为表出达文波特常数的极小集,在群G=C_(3)^(r)(r≤3)上A(G)是表出达文波特常数的极小集.Let G be an additive finite abelian group,let B(G)denote the set of all zero-sum sequences over G,and Ω is a subset of B(G).Let d_(Ω)(G)be the smallest integer t such that every sequence S of length greater than or equal to t over G has a subsequence inΩ.Let the minimum Ω of d_(Ω)(G)=t≥D(G)be the minimumΩof d_(Ω)(G)=t,if every proper subsetΩ_(1) of Ω has d_(Ω1)(G)>t,the minimumΩof dΩ(G)=D(G)is the minimal set of the minimal set of Davenport constants,and A(G)is the minimal set of Davenport constants over the group G=C_(3)^(r) (r≤3).

关 键 词：达文波特常数 极小集 零和序列 

分 类 号：O157.1[理学—数学]