Name
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 [R. Ahlswede and L. 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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.dam.2006.11.018 | Electronic Notes in Discrete Mathematics |
Keywords | Field | DocType |
n subsets,05d05,free family,geometric consequence,cone dependence-a basic combinatorial,n term,der mathematik sfb,diskrete strukturen,characteristic vector,universitat bielefeld,hypercube,positive linear combination,convex cone,52b05,large convex cone | Linear combination,Discrete mathematics,Family of sets,Combinatorics,Regular polygon,Mathematics,Eigenvalues and eigenvectors,Hypercube,Convex cone,Preprint | Journal |
Volume | Issue | ISSN |
156 | 9 | Discrete Applied Mathematics |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zoltán Füredi | 1 | 1237 | 233.60 |
| M. Ruszinkó | 2 | 230 | 35.16 |