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arXiv · 2605.21321

Arithmetic Properties of Overcolored Odd Partitions

M. P. Thejitha·S. N. Fathima
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Abstract

Let $\bar{a}_s(n)$ denote the number of partitions of $n$, wherein each odd part is multicolored (atmost $s\ge 1$ colors) and the first appearance of parts may be overlined. In this paper, we establish new families of congruences modulo powers of $2$ satisfied by $\bar{a}_s(n)$ for infinitely many $s$. Our approach builds upon generating function manipulations, Hecke eigenform theory and results of Newman.

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M. P. Thejitha, S. N. Fathima. 2026-05-20. Arithmetic Properties of Overcolored Odd Partitions. https://arxiv.org/abs/2605.21321

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