2 citations · 2 across the 5 of their papers we have counts for
9 papers
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 …
An extension of Gauss congruences for Apéry numbers
Ji-Cai Liu
Osburn, Sahu and Straub introduced the numbers: \begin{align*} A_n^{(r,s,t)}=\sum_{k=0}^n{n\choose k}^r{n+k\choose k}^s{2k\choose n}^t, \end{align*} for non-negative integers $n,r,…
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…
Two new -supercongruences arising from Carlitz's identity
Ji-Cai Liu, Wei-Wei Qi
From Carlitz's identity, we deduce two new -supercongruences modulo the square of a cyclotomic polynomial, which were originally conjectured by Guo. These results establish new…
Supercongruences involving Motzkin numbers and central trinomial coefficients
Ji-Cai Liu
Let and denote the th Motzkin number and the th central trinomial coefficient respectively. We prove that for any prime , \begin{align*} &\sum_{k=0}^{p-1}…