On supplementary difference sets
On supplementary difference sets
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关于补充差分集
DOI：
10.1007/bf01844498
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发表时间：
1972
影响因子：
0.8
通讯作者：
Jennifer Wallis
中科院分区：
文献类型：
--
作者：
Jennifer Wallis
给定一个有限无边群 V 和 V 的子集 S1, S2,...,Sn，则用 Ti 表示 Si 中所有元素之间可能存在的差异的总和（重复次数按倍数计算），用 T 表示所有 Ti 中成员的总和。如果 T 包含 V 中每个非零元素的次数相同，那么集合 S1、S2......、Sn 将被称为补充差集。我们将讨论这类集合的一些性质，给出一些存在性定理，并观察它们在构建哈达玛矩阵和平衡不完全块设计中的应用。学科 物理科学与数学 出版信息 Jennifer Seberry Wallis, On supplementary difference sets, Aequationes Mathematicae, 8, (1972), 242-257.该期刊文章可在 Research Online: http://ro.uow.edu.au/infopapers/943 Vol. 8, fase.3, 1972 Reprint from aequationes mathematicae BIRKHAUSER VERLAG BASEL On Supplementary Difference Sets JENNIFER WALLIS (New South Wales, Australia) pages 242-257 Given a finite abelian group V and subsets S1, S2, ...如果 T 包含了相同次数的 V 的每个非零子集，那么集合 S1> S2,"" Sn 将被称为补充差集。我们将讨论这类集合的一些性质，给出一些存在性定理，并观察它们在构建哈达玛矩阵和平衡不完全块设计中的应用。
Given a finite abelian group V and subsets S1, S2, ... ,Sn of V, write Ti for the totality of all the possible differences between elements of Si (with repetitions counted multiply) and T for the totality of members of all the Ti. If T contains each non-zero element of V the same number of times, then the sets S1, S2,...,Sn will be called supplementary difference sets. We discuss some properties for such sets, give some existence theorems and observe their use in the construction of Hadamard matrices and balanced incomplete block designs. Disciplines Physical Sciences and Mathematics Publication Details Jennifer Seberry Wallis, On supplementary difference sets, Aequationes Mathematicae, 8, (1972), 242-257. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/943 Vol. 8, fase. 3, 1972 Reprint from aequationes mathematicae BIRKHAUSER VERLAG BASEL On Supplementary Difference Sets JENNIFER WALLIS (New South Wales, Australia) pages 242-257 Given a finite abelian group V and subsets S1, S2, ... , Sn of V, write Ti for the totality of all the possible differences between elements of Si (with repetitions counted multiply) and T for the totality of members of all the T i• If T contains each non-zero dement of V the same number of times, then the sets S1> S2,"" Sn will be called supplementary difference sets. We discuss some properties for such sets, give some existence theorems and observe their use in the construction of Hadamard matrices and balanced incomplete block designs.