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arXiv · 2609.03926

Overcolored Partition $k$-tuples Restricted by Parity of the Parts

M. P. Thejitha·S. N. Fathima
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Abstract

In this paper, we study the combinatorial object $\bar{b}^k_{r,s}(n)$ which counts the overcolored partition $k$-tuples wherein both even and odd parts are colored with $r$ and $s$ colors, respectively. We extend results of Chacon and Sellers for several families of $r,s$ and $k$. We also establish divisibility properties for $\bar{b}^k_{r,s}(n)$ modulo prime $p$ and conclude with new congruences modulo powers of $2$. The techniques involved to obtain our results rely on theta function identities and modular forms.

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M. P. Thejitha, S. N. Fathima. 2026-09-03. Overcolored Partition $k$-tuples Restricted by Parity of the Parts. https://arxiv.org/abs/2609.03926

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