{"title":"乘法立方体和乘法自动机","authors":"JOHAN KOPRA","doi":"10.1017/etds.2024.44","DOIUrl":null,"url":null,"abstract":"We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers <jats:italic>p</jats:italic> and <jats:italic>q</jats:italic> in base <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000440_inline1.png\"/> <jats:tex-math> $pq$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multiplication cubes and multiplication automata\",\"authors\":\"JOHAN KOPRA\",\"doi\":\"10.1017/etds.2024.44\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers <jats:italic>p</jats:italic> and <jats:italic>q</jats:italic> in base <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S0143385724000440_inline1.png\\\"/> <jats:tex-math> $pq$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.\",\"PeriodicalId\":50504,\"journal\":{\"name\":\"Ergodic Theory and Dynamical Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ergodic Theory and Dynamical Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/etds.2024.44\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ergodic Theory and Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/etds.2024.44","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们将以前已知的模拟两个自然数 p 和 q 以 $pq$ 为基数相乘的二维乘法镶嵌系统扩展到高维乘法镶嵌系统。我们发展了这些系统的理论，并通过宏梯形运算将不同的乘法镶嵌系统相互连接起来，宏梯形运算可将一个镶嵌系统中的立方体粘合到另一个镶嵌系统的更大立方体中。巨型运算产生了拓扑共轭，以及在不同基数下执行正数乘法的细胞自动机之间的因子映射。
We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers p and q in base $pq$ to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.
期刊介绍：
Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.
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