On Multi-Color Partitions with Distinct Parts

Abstract

Given integers \(m \geq 2, r \geq 2\), let \(q_m(n), q_0^{(m)}(n), b_r^{(m)}(n)\) denote respectively the number of \(m\)-colored partitions of \(n\) into: distinct parts, distinct odd parts, and parts not divisible by \(r\).We obtain recurrences for each of the above-mentioned types of partition functions.