{"title":"论点和块基元设计在置换群下的不变性","authors":"Amin Saeidi","doi":"arxiv-2409.09730","DOIUrl":null,"url":null,"abstract":"In this paper, we present a method for constructing point primitive block\ntransitive $t$-designs invariant under finite groups. Furthermore, we\ndemonstrate that every point and block primitive $G$-invariant design can be\ngenerated using this method. Additionally, we establish the theoretical possibility of identifying all\nblock transitive $G$-invariant designs. However, in practice, the feasibility\nof enumerating all designs for larger groups may be limited by the\ncomputational complexity involved.","PeriodicalId":501407,"journal":{"name":"arXiv - MATH - Combinatorics","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On point and block primitive designs invariant under permutation groups\",\"authors\":\"Amin Saeidi\",\"doi\":\"arxiv-2409.09730\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a method for constructing point primitive block\\ntransitive $t$-designs invariant under finite groups. Furthermore, we\\ndemonstrate that every point and block primitive $G$-invariant design can be\\ngenerated using this method. Additionally, we establish the theoretical possibility of identifying all\\nblock transitive $G$-invariant designs. However, in practice, the feasibility\\nof enumerating all designs for larger groups may be limited by the\\ncomputational complexity involved.\",\"PeriodicalId\":501407,\"journal\":{\"name\":\"arXiv - MATH - Combinatorics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09730\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09730","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On point and block primitive designs invariant under permutation groups
In this paper, we present a method for constructing point primitive block
transitive $t$-designs invariant under finite groups. Furthermore, we
demonstrate that every point and block primitive $G$-invariant design can be
generated using this method. Additionally, we establish the theoretical possibility of identifying all
block transitive $G$-invariant designs. However, in practice, the feasibility
of enumerating all designs for larger groups may be limited by the
computational complexity involved.