Uniform decompositions of polytopes

Tom 33 / 2006

Daniel Berend, Luba Bromberg Applicationes Mathematicae 33 (2006), 243-252 MSC: 65D18, 60-08. DOI: 10.4064/am33-2-7

Streszczenie

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.

Autorzy

  • Daniel BerendDepartments of Mathematics and Computer Science
    Ben-Gurion University of the Negev
    Beer-Sheva 84105, Israel
    e-mail
  • Luba BrombergDepartment of Mathematics
    Ben-Gurion University of the Negev
    Beer-Sheva 84105, Israel

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