7 papers
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 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…
Rogers-Ramanujan Type Identities Involving Double Sums
Dandan Chen, Siyu Yin
We prove four new Rogers-Ramanujan-type identities for double series. They follow from the classical Rogers-Ramanujan identities using the constant term method and properties of Ro…
A conjecture of Gasper on -ultraspherical polynomials
Dandan Chen, Siyu Yin
In this paper we establish -orthogonality relation for the continuous -ultraspherical polynomials, which was considered by Gasper. Additionally, we evaluate a new -beta in…