منابع مشابه
Cutting a Polytope
We show that given two vertices of a polytope one cannot in general nd a hyperplane containing the vertices, that has two or more facets of the polytope in one closed half-space. Our result refutes a long-standing conjecture. We prove the result by constructing a 4-dimensional polytope that provides the counterexample. Also, we show that such a cutting hyperplane can be found for each pair of v...
متن کاملSilhouette of a random polytope
We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in R3 such that its average number of points is n. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is Θ( √ n).
متن کاملOn Moments of a Polytope
We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P ⊂ R is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal to the degree of the density function. Using this, we solve the inverse moment problem for the set of...
متن کاملThe Gomory-Chvátal Closure of a Non-Rational Polytope is a Rational Polytope
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متن کاملA Polytope Combinatorics for Semisimple Groups
Mirković and Vilonen discovered a canonical basis of algebraic cycles for the intersection homology of (the closures of the strata of) the loop Grassmannian. The moment map images of these varieties are a collection of polytopes, and they may be used to compute weight multiplicities and tensor product multiplicities for representations of a semisimple group. The polytopes are explicitly describ...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 1995
ISSN: 0046-5755,1572-9168
DOI: 10.1007/bf01265345