完成块大小为3的半帧频谱

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2022-09-13 DOI:10.1002/jcd.21856

H. Cao, D. Xu, Hao Zheng

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引用次数: 1

摘要

g - u型k -半框架是g - u (X, g，∑)型的k - GDD，其中块的集合∑可以写成一个不相交的并集∑= P∪Q，其中P被划分为X的并行类，Q被划分为空洞并行类，每个空洞并行类是X \ g对某个g∈g的一个划分。在本文中，我们将引入t -完美半框架的新概念，并利用它证明了群大小为偶数的g - u型3 -半框架的存在性。这就完成了群大小一致的3 -半框存在性的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Completing the spectrum of semiframes with block size three

A k ‐semiframe of type g u is a k ‐GDD of type g u ( X , G , ℬ ) , in which the collection of blocks ℬ can be written as a disjoint union ℬ = P ∪ Q , where P is partitioned into parallel classes of X and Q is partitioned into holey parallel classes, each holey parallel class being a partition of X \ G for some G ∈ G . In this paper, we will introduce a new concept of t ‐perfect semiframe and use it to prove the existence of a 3‐semiframe of type g u with even group size. This completes the proof of the existence of 3‐semiframes with uniform group size.

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来源期刊

Journal of Combinatorial Designs 数学-数学

CiteScore

1.60

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Combinatorial Designs is an international journal devoted to the timely publication of the most influential papers in the area of combinatorial design theory. All topics in design theory, and in which design theory has important applications, are covered, including: block designs, t-designs, pairwise balanced designs and group divisible designs Latin squares, quasigroups, and related algebras computational methods in design theory construction methods applications in computer science, experimental design theory, and coding theory graph decompositions, factorizations, and design-theoretic techniques in graph theory and extremal combinatorics finite geometry and its relation with design theory. algebraic aspects of design theory. Researchers and scientists can depend on the Journal of Combinatorial Designs for the most recent developments in this rapidly growing field, and to provide a forum for both theoretical research and applications. All papers appearing in the Journal of Combinatorial Designs are carefully peer refereed.