  In the first chapter of Shannon's "A Mathematical Theory of Communication,"
it is shown that the maximum entropy rate of an input process of a constrained
system is limited by the combinatorial capacity of the system. Shannon
considers systems where the constraints define regular languages and uses
results from matrix theory in his derivations. In this work, the regularity
constraint is dropped. Using generating functions, it is shown that the maximum
entropy rate of an input process is upper-bounded by the combinatorial capacity
in general. The presented results also allow for a new approach to systems with
regular constraints. As an example, the results are applied to binary sequences
that fulfill the (j,k) run-length constraint and by using the proposed
framework, a simple formula for the combinatorial capacity is given and a
maxentropic input process is defined.
