Constructing block designs with a prescribed automorphism group using genetic algorithm

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2022-03-22 DOI:10.1002/jcd.21838

Dean Crnković, Tin Zrinski

引用次数: 0

Abstract

We propose a method of constructing block designs which combine genetic algorithm and a method for constructing designs with a prescribed automorphism group using tactical decompositions (i.e., orbit matrices). We apply this method to construct new Steiner systems with parameters $S (2, 5, 45)$ and new symmetric designs with parameters (71, 15, 3).

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用遗传算法构造具有指定自同构群的块设计

我们提出了一种构建块设计的方法，该方法结合了遗传算法和一种使用战术分解（即轨道矩阵）构建具有指定自同构群的设计的方法。我们将此方法应用于构造参数为S（2，5，45）$S的新的Steiner系统（2，5，45）$和具有参数（71， 15， 3）。

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.