{"title":"共同的横向和强大的交换系统","authors":"Richard A. Brualdi","doi":"10.1016/S0021-9800(70)80084-9","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate properties of common transversals of two families of sets. Some structure theorems are proved, and we settle affirmatively a conjecture of L. Mirsky and H. Perfect concerning the existence of a common transversal for two families of sets.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 307-329"},"PeriodicalIF":0.0000,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80084-9","citationCount":"8","resultStr":"{\"title\":\"Common transversals and strong exchange systems\",\"authors\":\"Richard A. Brualdi\",\"doi\":\"10.1016/S0021-9800(70)80084-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We investigate properties of common transversals of two families of sets. Some structure theorems are proved, and we settle affirmatively a conjecture of L. Mirsky and H. Perfect concerning the existence of a common transversal for two families of sets.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"8 3\",\"pages\":\"Pages 307-329\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80084-9\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800849\",\"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/S0021980070800849","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We investigate properties of common transversals of two families of sets. Some structure theorems are proved, and we settle affirmatively a conjecture of L. Mirsky and H. Perfect concerning the existence of a common transversal for two families of sets.
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