5 papers
Truncated MacMahon-type -series in arithmetic progressions and Chebyshev expansions
Ji-Cai Liu
We study three finite families of MacMahon-type -series. The first is the arithmetic-progression family , which contains the usual truncated MacMahon serie…
Combinatorial proofs of several partition identities of Andrews and Merca
Ji-Cai Liu, Huan Liu
Based on a bijection due to Fu and Tang, we provide combinatorial proofs of several partition identities of Andrews and Merca. We also introduce two weights for partitions to exten…
On -regular partitions and Hickerson's identity
Ji-Cai Liu
Based on two involutions and a bijection, we completely determine the difference between the number of -regular partitions of into an even number of parts and into an odd…
A bijection proof of Andrews-Merca integer partition theorem
Ji-Cai Liu
Andrews and Merca [J. Combin. Theory Ser. A 203 (2024), Art. 105849] recently obtained two interesting results on the sum of the parts with the same parity in the partitions of …
A combinatorial approach to Berkovich type identities
Ji-Cai Liu
Motivated by Berkovich's nine -binomial identities involving the Legendre symbol , we establish a unified form of -binomial identities of this type through a c…