New results related to a conjecture of Manickam and Singhi
Abstract
In 1998 Manickam and Singhi conjectured that for every positive integer $d$ and every $n \ge 4d$, every set of $n$ real numbers whose sum is nonnegative contains at least $\binom {n-1}{d-1}$ subsets of size $d$ whose sums are nonnegative. In this paper we establish new results related to this conjecture. We also prove that the conjecture of Manickam and Singhi does not hold for $n=2d+2$.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 2006
- DOI:
- 10.48550/arXiv.math/0610977
- arXiv:
- arXiv:math/0610977
- Bibcode:
- 2006math.....10977C
- Keywords:
-
- Mathematics - Combinatorics;
- 05D05;
- 05A15
- E-Print:
- European Journal of Combinatorics Volume 29, Issue 2, February 2008, Pages 361-368