  This paper addresses the problem of finding $Q_{m,t}\left(n\right)$, the
number of possible ways to partition any member $n$ of the cyclic group
$\mathbb{Z}/m\mathbb{Z}$ into $t$ distinct parts. When $m$ is odd, it was
previously known that the number of partitions of the identity element $0\bmod
m$ with distinct parts is equal to the number of possible bi-color necklaces
with $m$ beads. This paper will expand upon this result by showing the
equivalence between $Q_{m,t}\left(n\right)$ and the number of bi-color
necklaces meeting certain periodicity requirements, even when $m$ is even.
