Block-Primitive Rank 3 t -Designs With Sporadic or Alternating Socle

IF 0.8 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2026-10-12 Epub Date: 2026-09-06 DOI:10.1002/jcd.70034

Suyun Ding, Xiaoqin Zhan

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引用次数: 0

Abstract

In this paper, we classify nontrivial $t$ - $(v, k, λ)$ designs with $t \geq 2$ and $v \geq 2 k$ admitting an automorphism group that acts primitively with rank 3 on the block set, under the assumption that the socle is a sporadic simple group or an alternating group. We show that, apart from the known symmetric examples, the only possibilities are the 2-, 3-, and 4-designs associated with the Mathieu groups $M_{22}$ and $M_{23}$ , together with a small number of 2-designs on $v \in {6, 10, 15}$ points arising from alternating groups.

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块状-原始等级3 t -具有零星或交替社会的设计

在本文中，我们将非平凡的t - (v)k ,λ)设计，t≥2和V≥2k承认在块集上存在秩为3的自同构群，假设该群是偶发简单群或交替群。我们证明，除了已知的对称例子外，唯一可能的是2-，3-，以及与Mathieu组m22和m23相关的4种设计，在v∈{6,10，由交替组得15分。

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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.