1-Rotational Balanced Incomplete Block Designs With Block Size Four and Arbitrary Index

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2026-05-28 Epub Date: 2026-03-26 DOI:10.1002/jcd.70013

Zian Zhang, Junling Zhou, Yanxun Chang

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引用次数: 0

Abstract

The necessary and sufficient conditions for the existence of 1-rotational balanced incomplete block designs with block size four and index unity have been determined to be $v \equiv 4 (\mod 12)$ and $v \neq 28$ [J. Comb. Theory, Ser. A 206 (2024) 105890]. This work completely determines the existence spectrum of 1-rotational balanced incomplete block designs with block size four and any index $λ \geq 2$ . To be specific, for $λ \geq 2$ and $v \geq 4$ , there exists a 1-rotational BIBD $(v, 4, λ)$ if and only if $λ (v - 1) \equiv 0 (\mod 3), λ v (v - 1) \equiv 0 (\mod 12)$ , and $(λ, v) \notin {(2, 7), (2, 10)}$ .

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1-旋转平衡不完全块设计与块大小为4和任意索引

确定了块大小为4且索引单位为1-旋转平衡不完全块设计存在的充分必要条件为v≡4 (模12)，且v≠28 [J]。合成杆。理论,爵士。[A][206(2024) 105890]。本文完全确定了块大小为4且任意指数λ≥2的1旋转平衡不完全块设计的存在谱。具体来说，当λ≥2，v≥4时，存在1旋转BIBD (v, 4，λ)当且仅当λ (v−(1)≡0 （mod 3）) ,λ v (v−1)≡0 (mod 12)，而(λ，V)∈(2)， 7)；(2)；10)}；

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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.