q-Binomial identities finder

IF 1.3 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-09-10 DOI:10.1016/j.aam.2025.102965

Hao Zhong, Leqi Zhao

引用次数: 0

Abstract

This paper presents a symbolic computation method for automatically transforming q-hypergeometric identities to q-binomial identities. Through this method, many previously proven q-binomial identities, including q-Saalschütz's formula and q-Suranyi's formula, are re-fund, and numerous new ones are discovered. Moreover, the generation of the identities is accompanied by the corresponding proofs. During the transformation process, different ranges of variable values and various combinations of q-Pochhammer symbols yield different identities. The algorithm maps variable constraints to positive elements in an ordered vector space and employs a backtracking method to provide the feasible variable constraints and q-binomial coefficient combinations for each step.

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q-二项式恒等式查找器

提出了一种将q-超几何恒等式自动转换为q-二项恒等式的符号计算方法。通过这种方法，许多先前证明的q-二项式等式，包括q- saalsch兹公式和q-Suranyi公式被重新证明，并发现了许多新的q-二项式等式。此外，这些恒等式的生成还伴随着相应的证明。在变换过程中，变量值的不同取值范围和q-Pochhammer符号的不同组合产生了不同的恒等式。该算法将变量约束映射到有序向量空间中的正元素，并采用回溯方法为每一步提供可行的变量约束和q-二项式系数组合。

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.