新的无限类2-色Steiner四元系统

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2022-05-19 DOI:10.1002/jcd.21845

Lijun Ji, Shuangqing Liu, Ye Yang

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引用次数: 0

摘要

1971年，Doyen和Vandensvel给出了一个特殊的二重构造，它给出了阶为v$v$（SQS）的2-色Steiner四重系统的直接构造（v）$（v）美元），对于所有v≠4$v\equiv 4$或8（mod 12）$8\，（\mathrm｛mod｝\，12）$。第一作者提出了一种基于双色烛台四重系统和s$s$-风扇设计的双色SQS的结构。在本文中，证明了一个2-色SQS（v）$（v）也存在，如果vlect 10（mod 12）$v\equiv 10\，（\mathrm｛mod｝\，12）$，或者如果v≠2（mod 24）$v\equiv 2\，（\mathrm｛mod｝\，24）$。

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New infinite classes of 2-chromatic Steiner quadruple systems

In 1971, Doyen and Vandensavel gave a special doubling construction that gives a direct construction of 2-chromatic Steiner quadruple system of order $v$ (SQS $(v)$ ) for all $v \equiv 4$ or $8 (\mod 12)$ . The first author presented a construction for 2-chromatic SQSs based on 2-chromatic candelabra quadruple systems and $s$ -fan designs. In this paper, it is proved that a 2-chromatic SQS $(v)$ also exists if $v \equiv 10 (\mod 12)$ , or if $v \equiv 2 (\mod 24)$ .

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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.