{"title":"一类极大二元单项式","authors":"Hajime Machida, J. Pantović","doi":"10.1109/ISMVL.2018.00022","DOIUrl":null,"url":null,"abstract":"The lattice of closed sets of monomials generated by a monomial of the form xy t over a finite field GF(k) is isomorphic to the lattice of divisors of k-1. If a monomial xy t generates a maximal element in that lattice, does it also generate a maximal element in the poset of closed sets generated by singleton binary monomials? This is the question studied in this paper. We have proven that over some finite fields xy 2 is a unique such monomial.","PeriodicalId":434323,"journal":{"name":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"One Class of Maximal Binary Monomials\",\"authors\":\"Hajime Machida, J. Pantović\",\"doi\":\"10.1109/ISMVL.2018.00022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The lattice of closed sets of monomials generated by a monomial of the form xy t over a finite field GF(k) is isomorphic to the lattice of divisors of k-1. If a monomial xy t generates a maximal element in that lattice, does it also generate a maximal element in the poset of closed sets generated by singleton binary monomials? This is the question studied in this paper. We have proven that over some finite fields xy 2 is a unique such monomial.\",\"PeriodicalId\":434323,\"journal\":{\"name\":\"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2018.00022\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2018.00022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The lattice of closed sets of monomials generated by a monomial of the form xy t over a finite field GF(k) is isomorphic to the lattice of divisors of k-1. If a monomial xy t generates a maximal element in that lattice, does it also generate a maximal element in the poset of closed sets generated by singleton binary monomials? This is the question studied in this paper. We have proven that over some finite fields xy 2 is a unique such monomial.
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