{"title":"替换的集合和不动点","authors":"F. Dekking","doi":"10.1090/bproc/132","DOIUrl":null,"url":null,"abstract":"<p>In this paper we introduce a technique to determine the sumset <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A plus upper A\">\n <mml:semantics>\n <mml:mrow>\n <mml:mi>A</mml:mi>\n <mml:mo>+</mml:mo>\n <mml:mi>A</mml:mi>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">A+A</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>, where <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\">\n <mml:semantics>\n <mml:mi>A</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">A</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is the indicator function of the 0’s occurring in a fixed point <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"x\">\n <mml:semantics>\n <mml:mi>x</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">x</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> of a substitution on the alphabet <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartSet 0 comma 1 EndSet\">\n <mml:semantics>\n <mml:mrow>\n <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo>\n <mml:mn>0</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mn>1</mml:mn>\n <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">\\{0,1\\}</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sumsets and fixed points of substitutions\",\"authors\":\"F. 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引用次数: 0
摘要
本文介绍了一种确定sumset a + a + a的方法，其中a a是在字母表{0,1}\{0,1\}上的替换的不动点x x上出现的0的指示函数。
In this paper we introduce a technique to determine the sumset A+AA+A, where AA is the indicator function of the 0’s occurring in a fixed point xx of a substitution on the alphabet {0,1}\{0,1\}.
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