  Restrictions of incidence-preserving path maps produce an oriented
hypergraphic All Minors Matrix-tree Theorems for Laplacian and adjacency
matrices. The images of these maps produce a locally signed graphic, incidence
generalization, of cycle covers and basic figures that correspond to
incidence-k-forests. When restricted to bidirected graphs the natural partial
ordering of maps results in disjoint signed boolean lattices whose minor
calculations correspond to principal order ideals. As an application, (1) the
determinant formula of a signed graphic Laplacian is reclaimed and shown to be
determined by the maximal positive-circle-free elements, and (2) spanning trees
are equivalent to single-element order ideals.
