{"title":"3 × 3永久物的警戒等级","authors":"Y. Shitov","doi":"10.1137/20m1349254","DOIUrl":null,"url":null,"abstract":"Let f be a homogeneous polynomial of degree d with coefficients in a field F satisfying char F = 0 or char F > d. The Waring rank of f is the smallest integer r such that f is a linear combination of r powers of F-linear forms. We show that the Waring rank of the polynomial x1 y2 z3 + x1 y3 z2 + x2 y1 z3 + x2 y3 z1 + x3 y1 z2 + x3 y2 z1 is at least 16, which matches the known upper bound.","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"The Waring Rank of the 3 x 3 Permanent\",\"authors\":\"Y. Shitov\",\"doi\":\"10.1137/20m1349254\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let f be a homogeneous polynomial of degree d with coefficients in a field F satisfying char F = 0 or char F > d. The Waring rank of f is the smallest integer r such that f is a linear combination of r powers of F-linear forms. We show that the Waring rank of the polynomial x1 y2 z3 + x1 y3 z2 + x2 y1 z3 + x2 y3 z1 + x3 y1 z2 + x3 y2 z1 is at least 16, which matches the known upper bound.\",\"PeriodicalId\":48489,\"journal\":{\"name\":\"SIAM Journal on Applied Algebra and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Algebra and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/20m1349254\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Algebra and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/20m1349254","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Let f be a homogeneous polynomial of degree d with coefficients in a field F satisfying char F = 0 or char F > d. The Waring rank of f is the smallest integer r such that f is a linear combination of r powers of F-linear forms. We show that the Waring rank of the polynomial x1 y2 z3 + x1 y3 z2 + x2 y1 z3 + x2 y3 z1 + x3 y1 z2 + x3 y2 z1 is at least 16, which matches the known upper bound.
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