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math.CO2025
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.…
math.CO2024
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 …
math.CO2024
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…