Year: 2026
Type: preprint
Abstract: In recent work, authors defined $\bar{b}^k_{r,s}(n)$ to be the number of overcolored partition $k$-tuples wherein both even and odd parts are colored with $r$ and $s$ colors, respectively. This function generalizes the overcubic partition $k$-tuples studied by Chacon and Sellers. The present work gives a uniform framework for studying congruences for $\bar{b}^k_{r,s}(n)$ modulo odd primes. For example, we prove that, for $n\ge 1$, \begin{align*} \bar{b}_{4,2}^4(5n)\equiv 0\pmod{5}. \end{align*}
Source: arXiv (Cornell University)
Authors: Thejitha, M. P., Fathima, S. N.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214727565