In 1988 Manickam and Singhi conjectured that for every positive integer $d$ and every $n\ge 4d$, every setof $n$ real numbers whose sum is non-negative contains at least $\binom{n−1}{d−1}$ subsets of size $d$ whose sums are non-negative. In this paper we make use of Hall’s matching theorem in order to study some numbers relatedto this conjecture.
New results related to a conjecture of Manickam and Singhi
Chiaselotti Giampiero;Infante Gennaro;Marino Giuseppe
2008-01-01
Abstract
In 1988 Manickam and Singhi conjectured that for every positive integer $d$ and every $n\ge 4d$, every setof $n$ real numbers whose sum is non-negative contains at least $\binom{n−1}{d−1}$ subsets of size $d$ whose sums are non-negative. In this paper we make use of Hall’s matching theorem in order to study some numbers relatedto this conjecture.File in questo prodotto:
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