14 papers
Sign Patterns in a Two Colored Partition Companion series
Aritram Dhar, Ankush Goswami, Mohit Tripathi
We study two closely related questions arising from the recent work of Andrews and El Bachraoui on the two-color partition series \[ S_1(q)=\sum_{n\ge0}s_1(n)q^n=\sum_{a\ge0}q^a(-q…
Separable integer partition classes and Slater's list -- II
Aritram Dhar, Ankush Goswami, Runqiao Li
Slater's list of Rogers-Ramanujan type identities remains a central source of striking series-product formulas in the theory of partitions and basic hypergeometric series. Although…
Weighted partitions with interval restrictions: exact formulas and a bivariate master identity
George E. Andrews, Mohamed El Bachraoui, Aritram Dhar +2
Let and be the signed partition functions introduced by Andrews and El Bachraoui for interval-restricted partitions whose parts greater than are controlle…
On Glaisher's Partition Theorem
George E. Andrews, Aritram Dhar
Glaisher's theorem states that the number of partitions of into parts which repeat at most times is equal to the number of partitions of into parts which are not divi…
Further Applications of Cubic -Binomial Transformations
Alexander Berkovich, Aritram Dhar
Consider \begin{align*} G(N,M;α,β,K,q) = \sum\limits_{j\in\mathbb{Z}}(-1)^jq^{\frac{1}{2}Kj((α+β)j+α-β)}\left[\begin{matrix}M+N\\N-Kj\end{matrix}\right]_{q}. \end{align*} In…
Separable integer partition classes and Slater's list -- I
Aritram Dhar, Ankush Goswami, Runqiao Li
Slater's list of Rogers-Ramanujan type identities consists of 130 series-product identities whose analytic proofs rely primarily on Bailey pair techniques. Although these identitie…