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...

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Detalles Bibliográficos
Autor principal: Lawrence, Jim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: [Gaithersburg, MD] : U.S. Dept. of Commerce, National Institute of Standards and Technology 2006
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4662502/
https://www.ncbi.nlm.nih.gov/pubmed/27274924
http://dx.doi.org/10.6028/jres.111.012
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author Lawrence, Jim
author_facet Lawrence, Jim
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description 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.
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spelling pubmed-46625022016-06-03 Three Rings of Polyhedral Simple Functions Lawrence, Jim J Res Natl Inst Stand Technol Article 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. [Gaithersburg, MD] : U.S. Dept. of Commerce, National Institute of Standards and Technology 2006 2006-04-01 /pmc/articles/PMC4662502/ /pubmed/27274924 http://dx.doi.org/10.6028/jres.111.012 Text en https://creativecommons.org/publicdomain/zero/1.0/ The Journal of Research of the National Institute of Standards and Technology is a publication of the U.S. Government. The papers are in the public domain and are not subject to copyright in the United States. Articles from J Res may contain photographs or illustrations copyrighted by other commercial organizations or individuals that may not be used without obtaining prior approval from the holder of the copyright.
spellingShingle Article
Lawrence, Jim
Three Rings of Polyhedral Simple Functions
title Three Rings of Polyhedral Simple Functions
title_full Three Rings of Polyhedral Simple Functions
title_fullStr Three Rings of Polyhedral Simple Functions
title_full_unstemmed Three Rings of Polyhedral Simple Functions
title_short Three Rings of Polyhedral Simple Functions
title_sort three rings of polyhedral simple functions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4662502/
https://www.ncbi.nlm.nih.gov/pubmed/27274924
http://dx.doi.org/10.6028/jres.111.012
work_keys_str_mv AT lawrencejim threeringsofpolyhedralsimplefunctions

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