Three Rings of Polyhedral Simple Functions.
We survey three ways to multiply elements of the additive subgroup of the group of real-valued functions on R(d) which is generated by the indicator functions of polyhedra. In the resulting commutative rings, identities often correspond to useful techniques of decomposition of polyhedra. We are led immediately to various interesting topics, including Ehrhart polynomials, mixed volumes, Gram's relation, and transversal characteristics.
Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030 and National Institute of Standards and Technology, Gaithersburg, MD 20899-8910.
Jim
J
Lawrence
Ehrhart polynomials; Gram’s relation; convex polyhedra; mixed volumes; transversal characteristic; valuation