One of the most useful principles of enumeration in discrete probability and combinatorial theory is the celebrated principle of·inclusion-exclusion (ef. Feller*, FrEchet, Riordan, Ryser). When… Expand

The following material is discussed in this paper: Incidence Coalgebras for PO sets; Reduced Boolean Coalgebras; Divided Powers Coalgebra; Dirichlet Coalgebra; Eulerian Coalgebra; Faa di Bruno… Expand

Introduction 1. The Buffon needle problem 2. Valuation and integral 3. A discrete lattice 4. The intrinsic volumes for parallelotopes 5. The lattice of polyconvex sets 6. Invariant measures on… Expand

It has been clear within the last ten years that combinatorial geometry, together with its order-theoretic counterpart, the geometric lattice, can serve to catalyze the whole field of combinatorial… Expand