Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4647780 | Discrete Mathematics | 2013 | 4 Pages |
Abstract
Given a rational a=p/q and N nonnegative d-dimensional real vectors u1,â¦,uN, we show that it is always possible to choose (dâ1)+â(pNâd+1)/qâ of them such that their sum is (componentwise) at least (p/q)(u1+â¯+uN). For fixed d and a, this bound is sharp if N is large enough. The method of the proof uses Carathéodory's theorem from linear programming.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ilya I. Bogdanov, Grigory R. Chelnokov,