Euclidean designs obtained from spherical embedding of coherent configurations

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2022-12-19 DOI:10.1002/jcd.21871

Aiguo Wang, Yan Zhu

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引用次数: 0

Abstract

Coherent configurations are a generalization of association schemes. Motivated by the recent study of Q-polynomial coherent configurations, in this paper, we study the spherical embedding of a Q-polynomial coherent configuration into some eigenspace by a primitive idempotent. We present a necessary and sufficient condition when the embedding becomes a Euclidean $t$ -design (on two concentric spheres) in terms of the Krein numbers for $t \leq 4$ . In addition, we obtain some Euclidean 2- or 3-designs from spherical embedding of coherent configurations including tight relative 4- or 5-designs in binary Hamming schemes and the union of derived designs of a tight 4-design in Hamming schemes.

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相干配置球面嵌入的欧氏设计

相干配置是关联方案的推广。受最近对Q多项式相干组态研究的启发，本文研究了Q多项式相干构型通过原幂等元球面嵌入到某个本征空间中的问题。当嵌入成为欧几里得t$t$-设计（在两个同心球上）时，我们根据t≤4的Krein数给出了一个充要条件$t\le 4$。此外，我们从相干配置的球面嵌入中获得了一些欧几里得2-或3-设计，包括二进制Hamming格式中的紧相对4-或5-设计以及Hamming方案中紧4-设计的导出设计的并集。

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.