A combinatorial approach to Berkovich type identities

2024/04/13 by Ji-Cai Liu, Liu, Ji-Cai
Engineering · Mathematics · #05A10 #05A17 #05A19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2404.08941

openalex publication_date 2024/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by Berkovich's nine q-binomial identities involving the Legendre symbol ((d)/(3)), we establish a unified form of q-binomial identities of this type through a combinatorial approach. This unified form includes Berkovich's nine identities as special cases. Many such identities can be also deduced from this unified form.

Related

• On the q-binomial identities involving the Legendre symbol modulo 3
• q-Rational and q-Real Binomial Coefficients
• A Probability Method to Prove Combinatorial Identities
• Combinatorial identities associated with a bivariate generating function for overpartition pairs
• Some Identities Involving Three Kinds of Counting Numbers