An Improvement on Triple Systems Without Two Types of Configurations

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2024-11-17 DOI:10.1002/jcd.21962

Liying Yu, Shuhui Yu, Lijun Ji

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引用次数: 0

Abstract

There are four nonisomorphic configurations of triples that can form a triangle in a three-uniform hypergraph, where the configurations $B$ and $D$ on ${1, 2, 3, 4, 5}$ consist of three triples $125, 134, 234$ and $123, 134, 235$ , respectively. Denote by ex $(n, D)$ and ex $(n, BD)$ the maximum number of triples in a three-uniform hypergraph on $n$ vertices which does not contain $D$ , both $B$ and $D$ , respectively. Recently, Frankl et al. used theorem of Gustavsson on sufficiently dense graphs to determine ex $(n, D)$ and ex $(n, BD)$ for all $n \geq n_{0}$ . In this note, we use packings and group divisible designs of block size 4 to remove the condition $n \geq n_{0}$ .

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无两种构型的三重系统的改进

在三均匀超图中有四种可以构成三角形的三元组的非同构构型，其中构型B ${\bf{B}}$和D ${\bf{D}}$在{1，$ $\{1,2,3,4,5\}$ $由三个三元组组成125，分别是134、234、125,134,234美元和123、134、235、123,134,235美元。用ex (n， D)$ (n,{\bf{D}})$和ex (n，D ${\bf{BD}})$ (n,{\bf{BD}})$在n$ n$顶点的三均匀超图中不包含D ${\bf{D}}$的最大三元组数，B ${\bf{B}}$和D ${\bf{D}}$。最近，Frankl等人利用Gustavsson定理在充分密集图上确定了ex (n， D)$ (n,{\bf{D}})$和ex (n，BD)$ (n,{\bf{BD}})$对于所有n≥n的0 $n\ge {n}_{0}$。在本文中，我们使用块大小为4的分组和组可分设计来消除n≥n 0 $n\ge {n}_{0}$的条件。

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.