  We demonstrate a method for listing all ordinary partitions of n as binary
words of length (n-1). The resulting family imbued with the hamming distance
yields subgraphs of the Hamming Graphs. The existence of a 2-Gray Code for
ordinary partitions follows from the fact that the graph (with the all 0s
partition omitted) is 2-connected. However, the graphs fail to be hamiltonian
for ordinary partitions when n > 7, ruling out the possibility of a Gray code
for all such flip graphs. We further investigate the degree distribution of the
graph for n, and provide computational evidence that this is a long-tailed
lognormal distribution. This conjecture connects to a closely related, and much
older, question of the distribution of the number of parts of a partition and
the same evidence suggests that this distribution is also lognormal for large
n. These methods extend to higher dimensional partitions of n which can be then
written as words of length (n-1) on d + 1 letters. The resulting graphs are
connected, proving that d-dimensional partitions allow a 3-Gray code.
