{"title":"一些平衡不完全块设计的非同构解。我","authors":"Vasanti N. Bhat, S.S. Shrikhande","doi":"10.1016/S0021-9800(70)80024-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we develop a method for generating non-isomorphic solutions of balanced incomplete block designs belonging to the series of symmetric designs with parameters (4<em>t</em>+3, 2<em>t</em>+1, <em>t</em>) and to the series with parameters (4<em>t</em>+4, 8<em>t</em>+6, 4<em>t</em>+3, 2<em>t</em>+2, 2<em>t</em>+1). We also prove a result about the number of non-isomorphic solutions of these designs as the parameter <em>t</em> tends to infinity.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"9 2","pages":"Pages 174-191"},"PeriodicalIF":0.0000,"publicationDate":"1970-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80024-2","citationCount":"5","resultStr":"{\"title\":\"Non-isomorphic solutions of some balanced incomplete block designs. I\",\"authors\":\"Vasanti N. Bhat, S.S. Shrikhande\",\"doi\":\"10.1016/S0021-9800(70)80024-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we develop a method for generating non-isomorphic solutions of balanced incomplete block designs belonging to the series of symmetric designs with parameters (4<em>t</em>+3, 2<em>t</em>+1, <em>t</em>) and to the series with parameters (4<em>t</em>+4, 8<em>t</em>+6, 4<em>t</em>+3, 2<em>t</em>+2, 2<em>t</em>+1). We also prove a result about the number of non-isomorphic solutions of these designs as the parameter <em>t</em> tends to infinity.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"9 2\",\"pages\":\"Pages 174-191\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80024-2\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800242\",\"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/S0021980070800242","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Non-isomorphic solutions of some balanced incomplete block designs. I
In this paper we develop a method for generating non-isomorphic solutions of balanced incomplete block designs belonging to the series of symmetric designs with parameters (4t+3, 2t+1, t) and to the series with parameters (4t+4, 8t+6, 4t+3, 2t+2, 2t+1). We also prove a result about the number of non-isomorphic solutions of these designs as the parameter t tends to infinity.
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