Arithmetic properties of $(\ell ,m)$-regular colored partitions

Yashas N., C. Shivashankar, S. Chandankumar

Let $b_{\ell ,m}^k(n)$ denotes the number of $k-$colored partitions of $n$ into parts that are not multiples of $\ell$ or $m$. We establish several congruence relations for $b_{\e…