  In a remarkable numerical analysis of the spectrum of states for a
spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo
and Fernandez-Borja found that the entropy of the black hole horizon increases
in what resembles discrete steps as a function of area. In the present article
we reformulate the combinatorial problem of counting horizon states in terms of
paths through a certain space. This formulation sheds some light on the origins
of this step-like behavior of the entropy. In particular, using a few extra
assumptions we arrive at a formula that reproduces the observed step-length to
a few tenths of a percent accuracy. However, in our reformulation the
periodicity ultimately arises as a property of some complicated process, the
properties of which, in turn, depend on the properties of the area spectrum in
loop quantum gravity in a rather opaque way. Thus, in some sense, a deep
explanation of the observed periodicity is still lacking.
