Summary: A hyper $m$-ary partition of an integer $n$ is defined to be a partition of $n$ where each part is a power of $m$ and each distinct power of $m$ occurs at most $m$ times. Let $h_{m}(n)$ denote the number of hyper $m$-ary partitions of $n$ and consider the resulting sequence. We show that the hyper $m_{1}$-ary partition sequence is a subsequence of the hyper $m_{2}$-ary partition sequence, for $2 \le m_{1} \le m_{2}$.

05A17

integer partition, hyper m-ary partition