{"title":"有限集上的半刚性等价关系","authors":"M. Miyakawa, M. Pouzet, I. Rosenberg, H. Tatsumi","doi":"10.1109/ISMVL.2008.47","DOIUrl":null,"url":null,"abstract":"A system R of equivalence relations on a set A (with at least 3 elements) is semirigid ;/ only the trivial opera tions (that is the projections and constant functions) preserve all members of R. To a system R of equivalence relations we associate a graph Gr. We observe that ifR is semirigid then the graph Gr is 2-connected. We show that the converse holds if all the members of R are atoms of the lattice E of equivalence relations on A. We present a notion of graphical composition of semirigid systems and show that it preserves semirigidity.","PeriodicalId":243752,"journal":{"name":"38th International Symposium on Multiple Valued Logic (ismvl 2008)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2008-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":"{\"title\":\"Semirigid Equivalence Relations on a Finite Set\",\"authors\":\"M. Miyakawa, M. Pouzet, I. Rosenberg, H. Tatsumi\",\"doi\":\"10.1109/ISMVL.2008.47\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A system R of equivalence relations on a set A (with at least 3 elements) is semirigid ;/ only the trivial opera tions (that is the projections and constant functions) preserve all members of R. To a system R of equivalence relations we associate a graph Gr. We observe that ifR is semirigid then the graph Gr is 2-connected. We show that the converse holds if all the members of R are atoms of the lattice E of equivalence relations on A. We present a notion of graphical composition of semirigid systems and show that it preserves semirigidity.\",\"PeriodicalId\":243752,\"journal\":{\"name\":\"38th International Symposium on Multiple Valued Logic (ismvl 2008)\",\"volume\":\"3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-05-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"11\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"38th International Symposium on Multiple Valued Logic (ismvl 2008)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2008.47\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"38th International Symposium on Multiple Valued Logic (ismvl 2008)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2008.47","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A system R of equivalence relations on a set A (with at least 3 elements) is semirigid ;/ only the trivial opera tions (that is the projections and constant functions) preserve all members of R. To a system R of equivalence relations we associate a graph Gr. We observe that ifR is semirigid then the graph Gr is 2-connected. We show that the converse holds if all the members of R are atoms of the lattice E of equivalence relations on A. We present a notion of graphical composition of semirigid systems and show that it preserves semirigidity.
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