Combinatorial Proofs of q-Series Identities

The q-Binomial Theorem and two Symmetric q-Identities

We notice two symmetric q-identities, which are special cases of the transformations of 2φ1 series in Gasper and Rahman’s book (Basic Hypergeometric Series, Cambridge University Press, 1990, p. 241). In this paper, we give combinatorial proofs of these two identities and the q-binomial theorem by using conjugation of 2-modular diagrams.

A tiling approach to eight identities of Rogers

Beginning in 1893, L. J. Rogers produced a collection of papers in which he considered series expansions of infinite products. Over the years, his identities have been given a variety of partition theoretic interpretations and proofs. These existing combinatorial techniques, however, do not highlight the similarities and the subtle differences seen in so many of these remarkable identities. It ...

2 00 1 Combinatorial proofs of q - series identities

Combinatorial proofs of a kind of binomial and q-binomial coefficient identities

We give combinatorial proofs of some binomial and q-binomial identities in the literature, such as ∞ ∑ k=−∞ (−1)kq(9k2+3k)/2 [ 2n n + 3k ] = (1 + q) n−1 ∏ k=1 (1 + q + q) (n ≥ 1),

A Combinatorial Proof of an Identity for the Divisor Generating Function

In this paper, we give combinatorial proofs and new generalizations of q-series identities of Dilcher and Uchimura related to divisor function. Some interesting combinatorial results related to partition and arm length are also presented.