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arXiv · 2603.12401

Proof of a Conjecture on Overcolored Partition Restricted by Parity of the Parts

Imdadul Hussain·Suparno Ghoshal·Arijit Jana
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Abstract

In a recent paper, Thejitha and Fathima introduced the overcolored partition function $\bar{a}_{r,s}(n)$, which enumerates overpartitions in which even parts may appear in one of $r$ colors and odd parts in one of $s$ colors, for fixed integers $r,s \geq 1$. They also proposed several conjectures concerning families of congruences modulo powers of $2$ for specific arithmetic progressions of $\bar{a}_{r,s}(n)$. In this paper, we provide an elementary proof of this conjecture that relies only on classical $q$-series manipulations and properties of Ramanujan's theta function.

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Imdadul Hussain, Suparno Ghoshal, Arijit Jana. 2026-03-12. Proof of a Conjecture on Overcolored Partition Restricted by Parity of the Parts. https://arxiv.org/abs/2603.12401

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