  The partition perimeter is a statistic defined to be one less than the sum of
the number of parts and the largest part. Recently, Amdeberhan, Andrews, and
Ballantine proved the following analog of Glaisher's theorem: for all $m \geq
2$ and $n \geq 1$, there are at least as many partitions with perimeter $n$ and
parts $\not \equiv 0 \pmod{m}$ as partitions with perimeter $n$ and parts
repeating fewer than $m$ times. In this work, we provide a combinatorial proof
of their theorem by relating the combinatorics of the partition perimeter to
that of compositions. Using this technique, we also show that a composition
theorem of Huang implies a refinement of another perimeter theorem of Fu and
Tang.
