投影空间中的Steiner三重系统和扩展集

IF 0.5 4区数学 Q3 MATHEMATICS Journal of Combinatorial Designs Pub Date : 2022-03-23 DOI:10.1002/jcd.21841

Zoltán Lóránt Nagy, Levente Szemerédi

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引用次数: 0

摘要

我们讨论了关于Steiner三重系统的点集的展开性质的几个极值问题。这一性质与子系统的结构密切相关，因为一个集是扩张的，当且仅当没有包含它的合适子系统时。我们给出了Steiner三系统中最小扩张集大小的尖锐上界，并证明了如果所有最小扩张集都很大，则所检查的三系统必须是投影空间。我们还证明了极小扩展集的大小不是Steiner三重系统的不变量。

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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Steiner triple systems and spreading sets in projective spaces

We address several extremal problems concerning the spreading property of point sets of Steiner triple systems. This property is closely related to the structure of subsystems, as a set is spreading if and only if there is no proper subsystem which contains it. We give sharp upper bounds on the size of a minimal spreading set in a Steiner triple system and show that if all the minimal spreading sets are large then the examined triple system must be a projective space. We also show that the size of a minimal spreading set is not an invariant of a Steiner triple system.

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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.