  We take the view that the area of a black hole's event horizon is quantized,
$A = l_P^2 \, (4 \ln 2) \, N$, and the associated degrees of freedom are finite
in number and of fermionic nature. We then investigate general aspects of the
entropy, $S_{BH}$, our main focus being black-hole self-similarity. We first
find a two-to-one map between the black hole's configurations and the ordered
partitions of the integer $N$. Hence we construct from there a composition law
between the sub-parts making the whole configuration space. This gives meaning
to black hole self-similarity, entirely within a single description, as a
phenomenon stemming from the well known self-similarity of the ordered
partitions of $N$. Finally, we compare the above to the well-known results on
the subleading (quantum) corrections, that necessarily require different
(quantum) statistical weights for the various configurations.
