An improved bound for the Manickam-Miklós-Singhi conjecture

Mykhaylo Tyomkyn

doi:10.1016/j.ejc.2011.07.006

An improved bound for the Manickam-Miklós-Singhi conjecture

Mykhaylo Tyomkyn^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We show that for n>k²(4elogk)^k, every set {x₁,;,x_n} of n real numbers with ∑_i=1ⁿx_i≥0 has at least (^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+k²)+k, proved by Manickam and Miklós [9] in 1987.

Original language	English
Pages (from-to)	27-32
Number of pages	6
Journal	European Journal of Combinatorics
Volume	33
Issue number	1
DOIs	https://doi.org/10.1016/j.ejc.2011.07.006
State	Published - Jan 2012
Externally published	Yes

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title = "An improved bound for the Manickam-Mikl{\'o}s-Singhi conjecture",

abstract = "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 Mikl{\'o}s [9] in 1987.",

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An improved bound for the Manickam-Miklós-Singhi conjecture

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