An improved bound for the Manickam-Miklós-Singhi conjecture

Mykhaylo Tyomkyn*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show that for n>k2(4elogk)k, every set {x1,;,xn} of n real numbers with ∑i=1nxi≥0 has at least (n-1k-1)k-element subsets of a non-negative sum. This is a substantial improvement on the best previously known bound of n>(k-1)(kk+k2)+k, proved by Manickam and Miklós [9] in 1987.

Original languageEnglish
Pages (from-to)27-32
Number of pages6
JournalEuropean Journal of Combinatorics
Issue number1
StatePublished - Jan 2012
Externally publishedYes


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