New infinite classes of 2‐chromatic Steiner quadruple systems

IF 0.5 4区数学 Q3 MATHEMATICS

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

L. Ji, Shuangqing Liu, Ye Yang

引用次数: 0

Abstract

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

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两色Steiner四重系的新无穷类

在1971年，Doyen和Vandensavel给出了一个特殊的加倍构造，给出了对所有v≡4$ v\equiv $ 4$或8 (mod 12)$ 8\，(\mathrm{mod}\，12)$的二阶Steiner四重系统v$ v$ (SQS (v)$ (v)$)的直接构造。第一作者提出了一种基于2色烛台四重系统和5 $ 5 $扇设计的2色SQSs结构。本文证明了当v≡10 (mod 12)$ v\equiv 10\，(\mathrm{mod}\，12)$，或v≡2 (mod 24)$ v\equiv 2\，(\mathrm{mod}\，24)$时，也存在二色SQS (v)$ (v)$。

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.