Continued fractions for q-deformed real numbers, {−1,0,1}-Hankel determinants, and Somos-Gale-Robinson sequences

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-09-24 DOI:10.1016/j.aam.2024.102788

Valentin Ovsienko , Emmanuel Pedon

引用次数: 0

Abstract

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

- 1, 0

and 1 only. These Hankel sequences satisfy Somos and Gale-Robinson recurrences.

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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

q 变形实数是具有整数系数的幂级数。我们研究了 q 变形实数的 Stieltjes 和 Jacobi 型续分数展开式，发现了许多此类续分数的新实例。我们还研究了相应的汉克尔行列式序列，并发现了一个无穷的幂级数族，其中几个汉克尔行列式的第一序列仅由-1、0 和 1 组成。这些汉克尔序列满足索莫斯和盖尔-罗宾逊递推规律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.