Large convex cones in hypercubes

Authors:
Zoltán Füredi;Miklós Ruszinkó
Affiliations:
Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Rényi Institute of Mathematics of the Hungarian Academy of Sciences, Budapest, P.O. Box 127, 1364, Hungary;Computer and Automation Research Institute of the Hungarian Academy of Sciences, Budapest, P.O. Box 63, 1518, Hungary
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 3
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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))2^n subsets of [n] and we give tight bounds on the o(1)2^n 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, Universitat Bielefeld, 2000] and the result has geometric consequences.