The existence of 2 3 ${2}^{3}$ -decomposable super-simple ( v , 4 , 6 ) $(v,4,6)$ -BIBDs

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2024-02-22 DOI:10.1002/jcd.21935

Huangsheng Yu, Jingyuan Chen, R. Julian R. Abel, Dianhua Wu

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引用次数: 0

Abstract

A design is said to be super-simple if the intersection of any two blocks has at most two elements. A design with index $t λ$ is said to be $λ^{t}$ -decomposable, if its blocks can be partitioned into nonempty collections $B_{i}$ , $1 \leq i \leq t$ , such that each $B_{i}$ with the point set forms a design with index $λ$ . In this paper, it is proved that there exists a $2^{3}$ -decomposable super-simple $(v, 4, 6)$ -BIBD (balanced incomplete block design) if and only if $v \geq 16$ and $v \equiv 1 (\mod 3)$ .

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存在23个可分解的超简单（v,4,6）$(v,4,6)$-BIBDs

如果任意两个图块的交集最多只有两个元素，则称该设计为超简单设计。如果一个有索引的设计的图块可以被分割为非空集合 , , , 这样每个集合与点集构成一个有索引的设计，那么这个设计就被称为可分解设计。本文证明，当且仅当和时，存在一个可分解的超简单 -BIBD（平衡不完全块设计）。

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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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.