  We investigate properties of the set of discrete Morse functions on a
simplicial complex as defined by Forman. It is not difficult to see that the
pairings of discrete Morse functions of a finite simplicial complex again form
a simplicial complex, the discrete Morse complex. It turns out that several
known results from combinatorial topology and enumerative combinatorics, which
previously seemed to be unrelated, can be re-interpreted in the setting of
these discrete Morse complexes.
