Mutual incidence matrix of two balanced incomplete block designs

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2024-06-17 DOI:10.1002/jcd.21949

Alexander Shramchenko, Vasilisa Shramchenko

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Abstract

We propose to consider a mutual incidence matrix $M$ of two balanced incomplete block designs built on the same finite set. In the simplest case, this matrix reduces to the standard incidence matrix of one block design. We find all eigenvalues of the matrices $M M^{T}$ and $M^{T} M$ and their eigenspaces.

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两个平衡不完全区块设计的互现矩阵

我们建议考虑建立在同一有限集合上的两个平衡不完全图块设计的互现矩阵 M $M$。在最简单的情况下，这个矩阵可以简化为一个图块设计的标准入射矩阵。我们将找到矩阵 M M T $M{M}^{T}$ 和 M T M ${M}^{T}M$ 的所有特征值及其特征空间。

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.