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).
作者
赵小越
吴雄华
Zhao Xiaoyue;Wu Xionghua(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China)
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
关键词
达文波特常数
极小集
零和序列
Davenport constant
the minimal set
zero-sum sequence
