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Three Rings of Polyhedral Simple Functions

Published

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

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 14, 2024)
Created March 1, 2006, Updated February 17, 2017