6 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…
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.…
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 …
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…