Large convex cones in hypercubes Original Research Article

A family of subsets of image is positive linear combination free if the characteristic vector of neither member is the positive linear combination of the characteristic vectors of some other ones. We construct a positive linear combination free family which contains image subsets of image and we give tight bounds on the image term. The problem was posed by Ahlswede and Khachatrian [Cone dependence—a basic combinatorial concept, Preprint 00-117, Diskrete Strukturen in der Mathematik SFB 343, Universität Bielefeld, 2000] and the result has geometric consequences.