5 papers · 1 filter
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 …
New proofs of theorems on q-orthogonal functions
Dandan Chen, Zhiguo Liu
In this paper, we establish a -integral formula by using the orthogonality relation, and also provide a new proof of the -orthogonality relation for the continuous -ultras…
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…