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Large convex cones in hypercubes |
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| Authors: | Zoltn Füredi Mikls Ruszink |
| Institution: | aDepartment of Mathematics, University of Illinois, Urbana, IL 61801, USA bRényi Institute of Mathematics of the Hungarian Academy of Sciences, Budapest, P.O. Box 127, 1364, Hungary cComputer and Automation Research Institute of the Hungarian Academy of Sciences, Budapest, P.O. Box 63, 1518, Hungary |
| Abstract: | A family of subsets of n] 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 (1-o(1))2n subsets of n] and we give tight bounds on the o(1)2n 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. |
| Keywords: | Hypercube Convex cone |
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