6 papers
On Bilateral Multiple Sums and Rogers-Ramanujan Type Identities
Dandan Chen, Tianjian Xu
We establish some new bilateral double-sum Rogers-Ramanujan identities involving parameters. As applications, these identities yield several new multi-sum Rogers-Ramanujan type ide…
Congruences modulo powers of for generalized Frobenius partitions
Dandan Chen, Siyu Yin
In 1984, Andrews introduced the family of partition functions \(cÏ_k(n)\), which counts the number of generalized Frobenius partitions of \(n\) with \(k\) colors. In previous work…
Congruences modulo powers of for -colored generalized Frobenius partitions
Dandan Chen, Siyu Yin
In , Andrews introduced the family of partition functions , which enumerate generalized Frobenius partitions of with colors. In , Gu, Wang, and Xia es…
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…
Congruences Modulo Powers of 7 for the Reciprocal Crank Parity Function
Dandan Chen
Amdeberhan and Merca recently studied arithmetic properties of the sequence , the reciprocal of the crank parity function, which counts the number of integer partitions of we…
Congruences modulo powers of for -elongated plane partitions
Dandan Chen, Tianjian Xu, Siyu Yin
The enumeration of -elongated plane partition diamonds has emerged as a generalization of the classical integer partition function . Congruences for modu…