  An oriented hypergraph is an oriented incidence structure that generalizes
and unifies graph and hypergraph theoretic results by examining its locally
signed graphic substructure. In this paper we obtain a combinatorial
characterization of the coefficients of the characteristic polynomials of
oriented hypergraphic Laplacian and adjacency matrices via a signed
hypergraphic generalization of basic figures of graphs. Additionally, we
provide bounds on the determinant and permanent of the Laplacian matrix,
characterize the oriented hypergraphs in which the upper bound is sharp, and
demonstrate that the lower bound is never achieved.
