6 papers · 1 filter
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…
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 identi…
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.…