An improved bound for the Manickam-Miklós-Singhi conjecture

Details An improved bound for the Manickam-Miklós-Singhi conjecture An improved bound for the Manickam-Miklós-Singhi conjecture

2010-11-12

arxiv.org/abs/1011.2803v1

Mathematics

Combinatorics

Scientific paper

We show that for $n>k(4e\log k)^k$ every set $\{x_1,..., x_n\}$ of $n$ real
numbers with $\sum_{i=0}^{n}x_i \geq 0$ has at least $\binom{n-1}{k-1}$
$k$-element subsets of a non-negative sum. This is a substantial improvement on
the best previously known bound of $n>(k-1)(k^k+k^2)+k$, proved by Manickam and
Mikl\'os \cite{MM} in 1987.

Affiliated with

Also associated with

No associations

Rating

An improved bound for the Manickam-Miklós-Singhi conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An improved bound for the Manickam-Miklós-Singhi conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An improved bound for the Manickam-Miklós-Singhi conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-203298