Complexes of discrete Morse functions

We investigate properties of the set of discrete Morse functions on a fixed simplicial complex as defined by Forman [5]. It is not difficult to see that the pairings of discrete Morse functions of Δ again form a simplicial complex, the complex of discrete Morse functions of Δ. 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 complexes of discrete Morse functions.