Combinatorial properties of convex cones in ![\mathbf R<sup>n</sup>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/e47f57960badd65d3c1d22ec173cceea.png)
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
is established.
![R_{2n}(m,3n)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/180ffffe71b1f8389be6e31ed3f5fe9e.png)
DOI Code:
10.1285/i15900932v19n1p25
Keywords:
Acute convex cone; Convex hull; Intersection graph; Ramsey number
Classification:
52A20; 52A35
Full Text: PDF