{"title":"λ-设计的一些结果","authors":"W.G. Bridges","doi":"10.1016/S0021-9800(70)80030-8","DOIUrl":null,"url":null,"abstract":"<div><p>A λ-design as introduced by Ryser [3] is a (0, 1)-square matrix with constant column inner products but <em>not</em> all column sums equal. Ryser has shown such a matrix to have two row sums and he constructs an infinite family of λ-designs called <em>H</em>-designs. This paper does three things: (1) generalizes Ryser's <em>H</em>-design construction to an arbitrary (ν, <em>k</em>, λ)-configuration, (2) establishes some additional general properties of λ-designs, and (3) determines all 4-designs.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 4","pages":"Pages 350-360"},"PeriodicalIF":0.0000,"publicationDate":"1970-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80030-8","citationCount":"22","resultStr":"{\"title\":\"Some results on λ-designs\",\"authors\":\"W.G. Bridges\",\"doi\":\"10.1016/S0021-9800(70)80030-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A λ-design as introduced by Ryser [3] is a (0, 1)-square matrix with constant column inner products but <em>not</em> all column sums equal. Ryser has shown such a matrix to have two row sums and he constructs an infinite family of λ-designs called <em>H</em>-designs. This paper does three things: (1) generalizes Ryser's <em>H</em>-design construction to an arbitrary (ν, <em>k</em>, λ)-configuration, (2) establishes some additional general properties of λ-designs, and (3) determines all 4-designs.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"8 4\",\"pages\":\"Pages 350-360\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80030-8\",\"citationCount\":\"22\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800308\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021980070800308","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A λ-design as introduced by Ryser [3] is a (0, 1)-square matrix with constant column inner products but not all column sums equal. Ryser has shown such a matrix to have two row sums and he constructs an infinite family of λ-designs called H-designs. This paper does three things: (1) generalizes Ryser's H-design construction to an arbitrary (ν, k, λ)-configuration, (2) establishes some additional general properties of λ-designs, and (3) determines all 4-designs.
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