  We provide a formula that expresses the number of (n-2)-gaps of a generic
digital n-object. Such a formula has the advantage to involve only a few simple
intrinsic parameters of the object and it is obtained by using a combinatorial
technic based on incidence structure and on the notion of free cells. This
approach seems suitable as a model for an automatic computation, and also allow
us to find some expressions for the maximum number of i-cells that bound or are
bounded by a fixed j-cell.
