关于确定性随机游走的记录和零点

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-09-09 DOI:10.1016/j.aam.2025.102963

Henk Bruin, Robbert Fokkink

{"title":"关于确定性随机游走的记录和零点","authors":"Henk Bruin, Robbert Fokkink","doi":"10.1016/j.aam.2025.102963","DOIUrl":null,"url":null,"abstract":"<div><div>We settle two questions on sequence A120243 in the OEIS that were raised by Clark Kimberling and partly solve a conjecture of Van de Lune and Arias de Reyna. We extend Kimberling's questions to the framework of deterministic random walks, automatic sequences, and linear recurrences. Our results indicate that there may be a deeper connection between these structures. In particular, we conjecture that the records of deterministic random walks are <em>ξ</em>-Ostrowski automatic for quadratic rotation numbers <em>ξ</em>.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"172 ","pages":"Article 102963"},"PeriodicalIF":1.3000,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the records and zeros of a deterministic random walk\",\"authors\":\"Henk Bruin, Robbert Fokkink\",\"doi\":\"10.1016/j.aam.2025.102963\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We settle two questions on sequence A120243 in the OEIS that were raised by Clark Kimberling and partly solve a conjecture of Van de Lune and Arias de Reyna. We extend Kimberling's questions to the framework of deterministic random walks, automatic sequences, and linear recurrences. Our results indicate that there may be a deeper connection between these structures. In particular, we conjecture that the records of deterministic random walks are <em>ξ</em>-Ostrowski automatic for quadratic rotation numbers <em>ξ</em>.</div></div>\",\"PeriodicalId\":50877,\"journal\":{\"name\":\"Advances in Applied Mathematics\",\"volume\":\"172 \",\"pages\":\"Article 102963\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0196885825001253\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885825001253","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们解决了Clark Kimberling提出的关于OEIS中A120243序列的两个问题，部分解决了Van de Lune和Arias de Reyna的猜想。我们将金伯林的问题扩展到确定性随机漫步、自动序列和线性递归的框架。我们的研究结果表明，这些结构之间可能存在更深层次的联系。特别地，我们推测确定性随机漫步的记录对于二次旋转数ξ是ξ- ostrowski自动的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the records and zeros of a deterministic random walk

We settle two questions on sequence A120243 in the OEIS that were raised by Clark Kimberling and partly solve a conjecture of Van de Lune and Arias de Reyna. We extend Kimberling's questions to the framework of deterministic random walks, automatic sequences, and linear recurrences. Our results indicate that there may be a deeper connection between these structures. In particular, we conjecture that the records of deterministic random walks are ξ-Ostrowski automatic for quadratic rotation numbers ξ.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.