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Journals and Conferences
A short and almost elementary proof of the Boros–Füredi–Bárány–Pach– Gromov theorem on the multiplicity of covering by simplices in R d is given. Let us give a proof of the… (More)
In this paper, we consider finite families of convex sets in R such that every d or fewer sets of the family have a common point. For some families of this type, we give upper bounds on the size of a… (More)
In this paper we prove that it is possible to inscribe a regular crosspolytope (multidimensional octahedron) into a smooth convex body in R, where d is an odd prime power. Some generalizations of… (More)
Introduction One possible way to express that the cube Q d = [0, 1] d has dimension d is to notice that it cannot be colored in d colors with arbitrarily small connected monochromatic components. A… (More)
For convex partitions of a convex body B we prove that we can put a homothetic copy of B into each set of the partition so that the sum of homothety coefficients is ≥ 1. In the plane the partition… (More)
We prove that any simple polytope (and some non-simple polytopes) in R 3 admits an inscribed regular octahedron.
We prove some analogues of the central point theorem and Tverberg’s theorem, where instead of points, we consider hyperplanes or affine flats of given dimension.
In this note we link symplectic and convex geometry by relating two seemingly different open conjectures: a symplectic isoperimetric-type inequality for convex domains, and Mahler’s conjecture on the… (More)