2 citations · 2 across the 16 of their papers we have counts for
16 papers
Versions of Andrews-Gordon Identities Revisited
Alexander Berkovich, Aritram Dhar
In this paper, we revisit the work of Berkovich and Paule on variants of the Andrews-Gordon identities. We find a generalization of their principal polynomial identity and, as a co…
Sign Patterns in a Two Colored Partition Companion series
Aritram Dhar, Ankush Goswami, Mohit Tripathi
We study three 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(…
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…
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…
Inequalities for the number of -hooks in two partition classes arising from sum-product identities
Aritram Dhar, Byungchan Kim, Eunmi Kim +1
Motivated by recent study on the number of -hooks in partitions arising from Euler's partition identity, we investigate the number of -hooks in the sets from the first Rogers…
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 this p…
Finite analogs of partition bias related to hook length two and a variant of Sylvester's map
Alexander Berkovich, Aritram Dhar
In this paper, we count the total number of hooks of length two in all odd partitions of and all distinct partitions of with a bound on the largest part of the partitions.…
On new minimal excludants of overpartitions related to some -series of Ramanujan
Aritram Dhar, Avi Mukhopadhyay, Rishabh Sarma
Inspired by Andrews' and Newman's work on the minimal excludant or "mex" of partitions, we define four new classes of minimal excludants for overpartitions and establish relations…
New Borwein-type conjectures
Alexander Berkovich, Aritram Dhar
Motivated by recent research of Wang and Krattenthaler, we use Maple to propose five new ``Borwein-type'' conjectures modulo and two new ``Borwein-type'' conjectures modulo …
Pfaff's Method Revisited
Aritram Dhar
In 1797, Pfaff gave a simple proof of a hypergeometric series summation formula which was much later reproved by Andrews in 1996. In the same paper, Andrews also proved o…
Extension of Bressoud's generalization of Borwein's conjecture and some exact results
Alexander Berkovich, Aritram Dhar
In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative -series…
On partitions with bounded largest part and fixed integral GBG-rank modulo primes
Alexander Berkovich, Aritram Dhar
In 2009, Berkovich and Garvan introduced a new partition statistic called the GBG-rank modulo which is a generalization of the well-known BG-rank. In this paper, we use the Lit…
A bijective proof of an identity of Berkovich and Uncu
Aritram Dhar, Avi Mukhopadhyay
The BG-rank BG() of an integer partition is defined as where is the number of odd-indexed odd parts and is the number of even-indexed odd par…
On identities of Bailey
Aritram Dhar
In this paper, we provide proofs of two summation formulas of Bailey using a identity of Carlitz. We show that in the limiting case, the two identitie…