{"title":"广义康托尔基础系统中的算术","authors":"Katarína Studenicová","doi":"10.1145/3637529.3637539","DOIUrl":null,"url":null,"abstract":"For alternate Cantor real base numeration systems we generalise the result of Frougny and Solomyak on arithmetics on the set of numbers with finite expansions. We generalise the notion of finiteness property, denoted (F). We also provide several necessary conditions, and comment on a sufficient condition of this property. The sufficient condition allows us to find a set of generalised Cantor bases with Property (F). The used construction also provides a method for performing addition of finite expansions in Cantor real bases.","PeriodicalId":41965,"journal":{"name":"ACM Communications in Computer Algebra","volume":"31 1","pages":"156 - 159"},"PeriodicalIF":0.4000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Arithmetics in Generalised Cantor Base Systems\",\"authors\":\"Katarína Studenicová\",\"doi\":\"10.1145/3637529.3637539\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For alternate Cantor real base numeration systems we generalise the result of Frougny and Solomyak on arithmetics on the set of numbers with finite expansions. We generalise the notion of finiteness property, denoted (F). We also provide several necessary conditions, and comment on a sufficient condition of this property. The sufficient condition allows us to find a set of generalised Cantor bases with Property (F). The used construction also provides a method for performing addition of finite expansions in Cantor real bases.\",\"PeriodicalId\":41965,\"journal\":{\"name\":\"ACM Communications in Computer Algebra\",\"volume\":\"31 1\",\"pages\":\"156 - 159\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Communications in Computer Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3637529.3637539\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Communications in Computer Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3637529.3637539","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
For alternate Cantor real base numeration systems we generalise the result of Frougny and Solomyak on arithmetics on the set of numbers with finite expansions. We generalise the notion of finiteness property, denoted (F). We also provide several necessary conditions, and comment on a sufficient condition of this property. The sufficient condition allows us to find a set of generalised Cantor bases with Property (F). The used construction also provides a method for performing addition of finite expansions in Cantor real bases.
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