1 citations · 1 across the 12 of their papers we have counts for
14 papers
Proofs of two conjectures of Berkovich and Dhar on hook lengths
Rong Chen
We prove stronger forms of two conjectures of Berkovich and Dhar concerning a coefficientwise inequality and pairs of hooks of length two in bounded partitions. The coefficientwise…
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 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…
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…
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 …
Congruences modulo powers of and for the crank and rank parity functions and related mock theta functions
Dandan Chen, Rong Chen, Frank Garvan
It is well known that Ramanujan conjectured congruences modulo powers of , and and for the partition function. These were subsequently proved by Watson (1938) and Atkin…
Congruence modulo 4 for Andrews' integer partition with even parts below odd parts
Dandan Chen, Rong Chen
We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of and furth…
Generating Functions of the Hurwitz Class Numbers Associated with Certain Mock Theta Functions
Dandan Chen, Rong Chen
We find the Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which is very close to certain mock theta functions. We also prove two com…
Congruences modulo powers of 5 for the rank parity function
Dandan Chen, Rong Chen, Frank Garvan
It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin (1967…
A proof of the mod unimodal sequence conjectures and related mock theta functions
Rong Chen, Frank Garvan
In 2012 Bryson, Ono, Pitman and Rhoades showed how the generating functions for certain strongly unimodal sequences are related to quantum modular and mock modular forms. They prov…
On Decomposition of as the Sum of Lambert Series and Cusp forms
Dandan Chen, Rong Chen
Based on the values of the Weierstrass elliptic function at , and the theory of modular forms on the arithmetic group $Γ_0(2…
On a class of elliptic functions associated with the even Dirichlet characters
Dandan Chen, Rong Chen
We construct a class of companion elliptic functions associated with the even Dirichlet characters. Using the well-known properties of the classical Weierstrass elliptic function $…