Uniform decompositions of polytopes

Daniel Berend, and Luba Bromberg. "Uniform decompositions of polytopes." Applicationes Mathematicae 33.2 (2006): 243-252. <http://eudml.org/doc/279057>.

@article{DanielBerend2006,
abstract = {We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier-Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression for the distribution function of a random variable of the form $∑_\{i=1\}^\{d\}c_\{i\}X_\{i\}$, where $(X₁,..., X_\{d\})$ is a random vector, uniformly distributed in a polytope.},
author = {Daniel Berend, Luba Bromberg},
journal = {Applicationes Mathematicae},
keywords = {convex polytope; -dimensional polytope; decomposition of polytope; distribution function; volume calculation; convex polytopes},
language = {eng},
number = {2},
pages = {243-252},
title = {Uniform decompositions of polytopes},
url = {http://eudml.org/doc/279057},
volume = {33},
year = {2006},
}

TY - JOUR
AU - Daniel Berend
AU - Luba Bromberg
TI - Uniform decompositions of polytopes
JO - Applicationes Mathematicae
PY - 2006
VL - 33
IS - 2
SP - 243
EP - 252
AB - We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier-Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression for the distribution function of a random variable of the form $∑_{i=1}^{d}c_{i}X_{i}$, where $(X₁,..., X_{d})$ is a random vector, uniformly distributed in a polytope.
LA - eng
KW - convex polytope; -dimensional polytope; decomposition of polytope; distribution function; volume calculation; convex polytopes
UR - http://eudml.org/doc/279057
ER -