Aritram Dhar

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20242026

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5 papers · 1 filter

math.CO2026

On Glaisher's Partition Theorem

George E. Andrews, Aritram Dhar

Glaisher's theorem states that the number of partitions of $n$ into parts which repeat at most $m - 1$ times is equal to the number of partitions of $n$ into parts which are not divi…

math.CO2025

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 $3$ and two new ``Borwein-type'' conjectures modulo $5$ …

math.CO2025

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 $q$ -series…

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 $n$ and all distinct partitions of $n$ with a bound on the largest part of the partitions.…

math.CO2024

A bijective proof of an identity of Berkovich and Uncu

Aritram Dhar, Avi Mukhopadhyay

The BG-rank BG( $I ¨ $ ) of an integer partition $I ¨ $ is defined as $BG (I ¨ ) := i - j$ where $i$ is the number of odd-indexed odd parts and $j$ is the number of even-indexed odd…