{"title":"多项式幂之间的依赖模式","authors":"B. Reznick","doi":"10.1090/dimacs/060/09","DOIUrl":null,"url":null,"abstract":"Let F = {f_1,...,f_r} be a family of polynomials and let the ticket of F, T(F), denote the set of integers m so that ${f_j^m}$ is linearly dependent. We show that |T(F)| \\le (r-1)(r-2)/2 and present many concrete examples, including one with r=6 and T(F) = {1,2,3,4,8,14}.","PeriodicalId":363327,"journal":{"name":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","volume":"455 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2001-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Patterns of Dependence Among Powers of Polynomials\",\"authors\":\"B. Reznick\",\"doi\":\"10.1090/dimacs/060/09\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let F = {f_1,...,f_r} be a family of polynomials and let the ticket of F, T(F), denote the set of integers m so that ${f_j^m}$ is linearly dependent. We show that |T(F)| \\\\le (r-1)(r-2)/2 and present many concrete examples, including one with r=6 and T(F) = {1,2,3,4,8,14}.\",\"PeriodicalId\":363327,\"journal\":{\"name\":\"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science\",\"volume\":\"455 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2001-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/dimacs/060/09\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/dimacs/060/09","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Patterns of Dependence Among Powers of Polynomials
Let F = {f_1,...,f_r} be a family of polynomials and let the ticket of F, T(F), denote the set of integers m so that ${f_j^m}$ is linearly dependent. We show that |T(F)| \le (r-1)(r-2)/2 and present many concrete examples, including one with r=6 and T(F) = {1,2,3,4,8,14}.
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