Three Rings of Polyhedral Simple Functions

Published

March 1, 2006

Author(s)

James F. Lawrence

Abstract

We survey three ways to multiply elements of the additive subgroup of the group of real--valued functions on Rd 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.

Citation

Journal of Research (NIST JRES) -

Volume

111

Issue

2

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

Keywords

convex polyhedra, Ehrhart polynomials, Gram's relation, mixed volumes, transversal characteristic, valuation

Citation

Lawrence, J. (2006), Three Rings of Polyhedral Simple Functions, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed April 3, 2025)