小Desarguesian投影平面上最小分块集的分类

IF 0.5 4区数学 Q3 MATHEMATICS

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

Kris Coolsaet, Arne Botteldoorn, Veerle Fack

{"title":"小Desarguesian投影平面上最小分块集的分类","authors":"Kris Coolsaet, Arne Botteldoorn, Veerle Fack","doi":"10.1002/jcd.21842","DOIUrl":null,"url":null,"abstract":"<p>A full classification (up to equivalence) of all minimal blocking sets in Desarguesian projective planes of order <math>\n <mrow>\n \n <mrow>\n <mo>≤</mo>\n \n <mn>8</mn>\n </mrow>\n </mrow></math> 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.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"30 8","pages":"561-580"},"PeriodicalIF":0.5000,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Classification of minimal blocking sets in small Desarguesian projective planes\",\"authors\":\"Kris Coolsaet, Arne Botteldoorn, Veerle Fack\",\"doi\":\"10.1002/jcd.21842\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A full classification (up to equivalence) of all minimal blocking sets in Desarguesian projective planes of order <math>\\n <mrow>\\n \\n <mrow>\\n <mo>≤</mo>\\n \\n <mn>8</mn>\\n </mrow>\\n </mrow></math> 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.</p>\",\"PeriodicalId\":15389,\"journal\":{\"name\":\"Journal of Combinatorial Designs\",\"volume\":\"30 8\",\"pages\":\"561-580\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Designs\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jcd.21842\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Designs","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jcd.21842","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

用计算机对≤8阶的Desarguesian投影平面上的所有极小分块集进行了完全分类（直至等价）。根据最小阻塞集的大小和自同构群的阶，将得到的最小阻塞集数制成表格。对于具有较大自同构群的最小分块集，给出了显式描述。这些结果中的一些也可以推广到更高阶的Desarguesian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。

查看原文本刊更多论文

Classification of minimal blocking sets in small Desarguesian projective planes

A full classification (up to equivalence) of all minimal blocking sets in Desarguesian projective planes of order $\leq 8$ 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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.