{"title":"On Cobham's theorem","authors":"F. Durand, M. Rigo","doi":"10.4171/Automata-2/4","DOIUrl":null,"url":null,"abstract":"In this chapter we essentially focus on the representation of non-negative integers in a given numeration system. The main role of such a system --- like the usual integer base $k$ numeration system --- is to replace numbers or more generally sets of numbers by their corresponding representations, {\\em i.e.}, by words or by languages. First we consider integer base numeration systems to present the main concepts but rapidly we will introduce non-standard systems and their relationships with substitutions.","PeriodicalId":267596,"journal":{"name":"Handbook of Automata Theory","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Handbook of Automata Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/Automata-2/4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
In this chapter we essentially focus on the representation of non-negative integers in a given numeration system. The main role of such a system --- like the usual integer base $k$ numeration system --- is to replace numbers or more generally sets of numbers by their corresponding representations, {\em i.e.}, by words or by languages. First we consider integer base numeration systems to present the main concepts but rapidly we will introduce non-standard systems and their relationships with substitutions.