20 citations · 20 across the 10 of their papers we have counts for
11 papers
On b-ary binomial coefficients with negative entries
Lin Jiu, Diane Y. H. Shi
Abstract. We generalize the -ary binomial coefficients with negative entries, which is based on the generating function obtained in early work. Besides an explicit expression in…
Combinatorial Proofs of Two Overpartition Theorems Connected by a Universal Mock Theta Function
Doris D. M. Sang, Diane Y. H. Shi
In 2015, Bringmann, Lovejoy and Mahlburg considered certain kinds overpartitions, which can been seen as the overpartition analogue of Schur's partition. The motivation of their wo…
Parity Considerations in Rogers-Ramanujan-Gordon Type Overpartitions
Doris D. M. Sang, Diane Y. H. Shi
In 2010, Andrews considers a variety of parity questions connected to classical partition identities of Euler, Rogers, Ramanujan and Gordon. As a large part in his paper, Andrews c…
Congruences modulo for Rogers--Ramanujan--Gordon type overpartitions
Doris D. M. Sang, Diane Y. H. Shi
In a recent work, Andrews defined the singular overpartitions with the goal of presenting an overpartition analogue to the theorems of Rogers--Ramanujan type for ordinary partition…
Orthogonal Polynomials and Lattice Path Interpretation for Higher-order Euler Polynomials
Lin Jiu, Diane Yahui Shi
We study the higher-order Euler polynomials and give the corresponding monic orthogonal polynomials, which are Meixner-Pollaczek polynomials with certain arguments and constant fac…
Overpartitions Identities Involving Gaps and Weights
Jeremy J. F. Guo, Doris D. M. Sang, Diane Y. H. Shi
In this paper, we find an identity which connects the overpartition function and the function of Rogers--Ramanujan--Gordon type overpartitions by considering the weights and gaps.…
Matrix Representation for Multiplicative Nested Sums
Lin Jiu, Diane Yahui Shi
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the ind…
An Overpartition Analogue of Bressoud's Theorem of Rogers-Ramanujan Type
William Y. C. Chen, Doris D. M. Sang, Diane Y. H. Shi
For , let denote the number of partitions of such that part 1 appears at most times, two consecutive integers l and appear at most …
The Rogers-Ramanujan-Gordon Theorem for Overpartitions
William Y. C. Chen, Doris D. M. Sang, Diane Y. H. Shi
Let be the number of partitions of with certain difference condition and let be the number of partitions of with certain congruence condition. The…
Anti-lecture Hall Compositions and Overpartitions
William Y. C. Chen, Doris D. M. Sang, Diane Y. H. Shi
We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k-2 equals the number of overpartitions of n with non-overlined parts not congruen…
Involutions for Rogers-Ramanujan-Gordon Type Identities with Parity Restrictions
William Y. C. Chen, Doris D. M. Sang, Diane Y. H. Shi
We find involutions for three Rogers-Ramanujan-Gordon type identities obtained by Andrews on the generating functions for partitions with part difference and parity restrictions.