Uniform decompositions of polytopes
Volume 33 / 2006
Applicationes Mathematicae 33 (2006), 243-252
MSC: 65D18, 60-08.
DOI: 10.4064/am33-2-7
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 $\sum_{i=1}^{d}c_{i}X_{i}$, where $(X_{1},\ldots ,X_{d})$ is a random vector, uniformly distributed in a polytope.
