This last chapter of the book is devoted to the study of the special case of Forman’s combinatorial gradient vector fields on regular Lefschetz complexes. In this situation, one can show that the associated connection matrix is uniquely determined and in fact can be determined in a direct way. This is accomplished in a number of steps. We begin by recalling basic properties of combinatorial vectors in the sense of Forman, before we present the definition and basic properties of his concept of combinatorial flow. After discussing the long-term limit of the latter, we can finally explain how it can be used to obtain the unique connection matrix in this setting. The uniqueness part of the assertion will rely heavily on the singleton partition. We would like to point out that throughout this section, we consider a very specific class of multivector fields, namely combinatorial gradient vector fields and the Morse decompositions consisting of critical vectors. In this specific setting, we will be able to establish both the existence of the Conley complex and the uniqueness of the associated connection matrix directly. Thus, we will obtain results which are valid on arbitrary regular Lefschetz complexes.