11 papers
Indefinite theta vectors and generalized Nahm sums of arbitrary rank
Dandan Chen, Siyu Yin
We construct indefinite theta representations for a family of signed generalized Nahm sums of arbitrary rank \(r\geq2\). After explicit normalization and boundary correction, one s…
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 generalized Frobenius partitions
Dandan Chen, Siyu Yin
In 1984, Andrews introduced the family of partition functions \(cϕ_k(n)\), which counts the number of generalized Frobenius partitions of \(n\) with \(k\) colors. In previous work,…
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 -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…
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 est…
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…