  In this note we provide a combinatorial interpretation for the powers of the
hypergraph Laplacians. Our motivation comes from the discrete formulation of
quantum mechanics and thermodynamics in the case of finite graphs, which
suggest a natural extension to simplicial and CW-complexes. With this
motivation, we also define generalizations of the odd Laplacian which is
specific to hypergraphs arising from CW-complexes. We then provide a
combinatorial interpretation for the powers of these Laplacians.
