{"title":"二次ε-CNS 多项式的特征","authors":"Borka Jadrijević , Kristina Miletić","doi":"10.1016/j.jnt.2024.04.007","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we give characterization of quadratic <em>ε</em>-canonical number system (<em>ε</em>−CNS) polynomials for all values <span><math><mi>ε</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials (<span><math><mi>ε</mi><mo>=</mo><mn>0</mn></math></span>) and quadratic SCNS polynomials (<span><math><mi>ε</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span>). This result is a consequence of our new characterization results of <em>ε</em>-shift radix systems (<em>ε</em>−SRS) in the two-dimensional case and their relation to quadratic <em>ε</em>−CNS polynomials.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characterization of quadratic ε−CNS polynomials\",\"authors\":\"Borka Jadrijević , Kristina Miletić\",\"doi\":\"10.1016/j.jnt.2024.04.007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we give characterization of quadratic <em>ε</em>-canonical number system (<em>ε</em>−CNS) polynomials for all values <span><math><mi>ε</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials (<span><math><mi>ε</mi><mo>=</mo><mn>0</mn></math></span>) and quadratic SCNS polynomials (<span><math><mi>ε</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span>). This result is a consequence of our new characterization results of <em>ε</em>-shift radix systems (<em>ε</em>−SRS) in the two-dimensional case and their relation to quadratic <em>ε</em>−CNS polynomials.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001057\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24001057","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we give characterization of quadratic ε-canonical number system (ε−CNS) polynomials for all values . Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials () and quadratic SCNS polynomials (). This result is a consequence of our new characterization results of ε-shift radix systems (ε−SRS) in the two-dimensional case and their relation to quadratic ε−CNS polynomials.
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