$q$-Binomial Identities Finder
Hao Zhong, Leqi Zhao

TL;DR
This paper introduces a symbolic computation method that automatically transforms $q$-hypergeometric identities into $q$-binomial identities, re-establishes known formulas, discovers new identities, and provides proofs through an algorithmic approach.
Contribution
The paper presents a novel algorithmic method for transforming and discovering $q$-binomial identities from $q$-hypergeometric identities, including proof generation.
Findings
Re-derivation of known $q$-binomial identities like $q$-Saalsch"utz's formula
Discovery of numerous new $q$-binomial identities
Automated proof generation for the identities
Abstract
This paper presents a symbolic computation method for automatically transforming -hypergeometric identities to -binomial identities. Through this method, many previously proven -binomial identities, including -Saalsch\"utz's formula and -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 -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 -binomial coefficient combinations for each step.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgorithms and Data Compression · Coding theory and cryptography · Polynomial and algebraic computation
