6 papers
Two-colored generalized Frobenius partitions and minimal-excludant sums over bipartitions
Rong Chen, Kang-Yu Wang, Yi-ning Wang
Let $\cpsi_{2,a}(n)$ denote the number of -colored Frobenius partitions of weight , where the two rows have prescribed length difference. We study the two cases and…
A Generalization of the Amdeberhan-Andrews-Ballantine Conjecture
Rong Chen, Tianjian Xu
In this paper, we prove a generalization of a conjecture of Amdeberhan, Andrews, and Ballantine on double Lambert series. Motivated by a question raised by Cui, Kumar, and Singh co…
A conjecture of Radu and Sellers on congruences modulo powers of 2 for broken 3-diamond partitions
Dandan Chen, Rong Chen, Siyu Yin
In 2007, Andrews and Paule introduced the family of functions , which enumerate the number of broken -diamond partitions for a fixed positive integer . In 2013, Radu…
A generalization of the Mordell integral
Dandan Chen, Rong Chen, Sander Zwegers
We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD t…
Combinatorial proofs for partitions with repeated smallest part
Dandan Chen, Rong Chen, Mengjie Zhao
Recently, Andrews and El Bachraoui considered the number of integer partitions whose smallest part is repeated exactly times and the remaining parts are not repeated. They pres…
On the total number of ones associated with cranks of partitions modulo 11
Dandan Chen, Rong Chen, Siyu Yin
In 2021, Andrews mentioned that George Beck introduced partition statistics , which denote the total number of ones in the partition of with crank congruent to …