Classification of minimal blocking sets in small Desarguesian projective planes

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Combinatorial Designs Pub Date : 2022-03-31 DOI:10.1002/jcd.21842

K. Coolsaet, Arne Botteldoorn, V. Fack

引用次数: 0

Abstract

A full classification (up to equivalence) of all minimal blocking sets in Desarguesian projective planes of order ≤ 8 was obtained by computer. The resulting numbers of minimal blocking sets are tabulated according to size of the set and order of the automorphism group. For the minimal blocking sets with the larger automorphism groups explicit descriptions are given. Some of these results can also be generalised to Desarguesian projective planes of higher order.

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小Desarguesian投影平面上最小块集的分类

用计算机得到了≤8阶的Desarguesian投影平面上所有最小块集的完全分类(达到等价)。根据最小块集的大小和自同构群的顺序，将得到的最小块集的个数制成表格。对于具有较大自同构群的最小块集，给出了显式描述。其中的一些结果也可以推广到高阶的德格赖投影平面。

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.