arXiv Analytics

Sign in

arXiv:math/0610977 [math.CO]AbstractReferencesReviewsResources

New results related to a conjecture of Manickam and Singhi

G. Chiaselotti, G. Infante, G. Marino

Published 2006-10-31Version 1

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 $n=2d+2$.

Related articles: Most relevant | Search more
arXiv:math/0508537 [math.CO] (Published 2005-08-26)
On a conjecture of Widom
arXiv:math/9811108 [math.CO] (Published 1998-11-18, updated 1998-11-19)
Proof of a Conjecture of Chan, Robbins, and Yuen
arXiv:math/9901040 [math.CO] (Published 1999-01-09)
A conjecture about partitions