{"title":"q 个变形实数的连续分数、{-1,0,1}-汉克尔行列式和索莫斯-盖尔-罗宾逊序列","authors":"Valentin Ovsienko , Emmanuel Pedon","doi":"10.1016/j.aam.2024.102788","DOIUrl":null,"url":null,"abstract":"<div><div><em>q</em>-deformed real numbers are power series with integer coefficients. We study Stieltjes and Jacobi type continued fraction expansions of <em>q</em>-deformed real numbers and find many new examples of such continued fractions. We also investigate the corresponding sequences of Hankel determinants and find an infinite family of power series for which several of the first sequences of Hankel determinants consist of <span><math><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn></math></span> and 1 only. These Hankel sequences satisfy Somos and Gale-Robinson recurrences.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0196885824001209/pdfft?md5=8ffb0f6262c5c3186d8020047fccd544&pid=1-s2.0-S0196885824001209-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Continued fractions for q-deformed real numbers, {−1,0,1}-Hankel determinants, and Somos-Gale-Robinson sequences\",\"authors\":\"Valentin Ovsienko , Emmanuel Pedon\",\"doi\":\"10.1016/j.aam.2024.102788\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div><em>q</em>-deformed real numbers are power series with integer coefficients. We study Stieltjes and Jacobi type continued fraction expansions of <em>q</em>-deformed real numbers and find many new examples of such continued fractions. We also investigate the corresponding sequences of Hankel determinants and find an infinite family of power series for which several of the first sequences of Hankel determinants consist of <span><math><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn></math></span> and 1 only. These Hankel sequences satisfy Somos and Gale-Robinson recurrences.</div></div>\",\"PeriodicalId\":50877,\"journal\":{\"name\":\"Advances in Applied Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0196885824001209/pdfft?md5=8ffb0f6262c5c3186d8020047fccd544&pid=1-s2.0-S0196885824001209-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0196885824001209\",\"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/S0196885824001209","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Continued fractions for q-deformed real numbers, {−1,0,1}-Hankel determinants, and Somos-Gale-Robinson sequences
q-deformed real numbers are power series with integer coefficients. We study Stieltjes and Jacobi type continued fraction expansions of q-deformed real numbers and find many new examples of such continued fractions. We also investigate the corresponding sequences of Hankel determinants and find an infinite family of power series for which several of the first sequences of Hankel determinants consist of and 1 only. These Hankel sequences satisfy Somos and Gale-Robinson recurrences.
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.
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