{"title":"在 HD0L 系统的语言中，无限制指数的基元字的数量是有限的","authors":"Karel Klouda, Štěpán Starosta","doi":"10.1016/j.jcta.2024.105904","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>H</em> be an HD0L-system. We show that there are only finitely many primitive words <em>v</em> with the property that <span><math><msup><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>, for all integers <em>k</em>, is an element of the factorial language of <em>H</em>. In particular, this result applies to the set of all factors of a morphic word. We provide a formalized proof in the proof assistant Isabelle/HOL as part of the Combinatorics on Words Formalized project.</p></div>","PeriodicalId":50230,"journal":{"name":"Journal of Combinatorial Theory Series A","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The number of primitive words of unbounded exponent in the language of an HD0L-system is finite\",\"authors\":\"Karel Klouda, Štěpán Starosta\",\"doi\":\"10.1016/j.jcta.2024.105904\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>H</em> be an HD0L-system. We show that there are only finitely many primitive words <em>v</em> with the property that <span><math><msup><mrow><mi>v</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span>, for all integers <em>k</em>, is an element of the factorial language of <em>H</em>. In particular, this result applies to the set of all factors of a morphic word. We provide a formalized proof in the proof assistant Isabelle/HOL as part of the Combinatorics on Words Formalized project.</p></div>\",\"PeriodicalId\":50230,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series A\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series A\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0097316524000438\",\"RegionNum\":2,\"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":"Journal of Combinatorial Theory Series A","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0097316524000438","RegionNum":2,"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
设 H 是一个 HD0L 系统。我们证明，对于所有整数 k，只有有限多个原始词 v 具有这样的性质：vk 是 H 的因子语言的一个元素。我们在证明助手 Isabelle/HOL 中提供了形式化证明，这是词上组合论形式化项目的一部分。
The number of primitive words of unbounded exponent in the language of an HD0L-system is finite
Let H be an HD0L-system. We show that there are only finitely many primitive words v with the property that , for all integers k, is an element of the factorial language of H. In particular, this result applies to the set of all factors of a morphic word. We provide a formalized proof in the proof assistant Isabelle/HOL as part of the Combinatorics on Words Formalized project.
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.
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