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Combinatorial properties of convex cones in  \mathbf R<sup>n</sup>


Abstract


In this paper we obtain sets of conditions under which the convex hull of a family of convex copies is an acute cone. Some intersectional results for families of convex sets there are also given. Finally, using two combinatorial results concerning families of convex cones, a lower bound for the Ramsey numbers R_{2n}(m,3n) is established.

DOI Code: 10.1285/i15900932v19n1p25

Keywords: Acute convex cone; Convex hull; Intersection graph; Ramsey number

Classification: 52A20; 52A35

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