Skip to main content

NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.

Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.

U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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 October 14, 2025)

Issues

If you have any questions about this publication or are having problems accessing it, please contact [email protected].

Created March 1, 2006, Updated February 17, 2017
Was this page helpful?