Let $a_1,\ldots,a_n$ be $n$ real numbers with non negative sum. We showthat if $n\ge12$ there exist at least $n-1\choose 2$ subsets of$\{a_1,\ldots,a_n\}$ with three elements which have non--negative sum.
A method to count the positive 3-subsets in a set of real numbers with non negative sum
MARINO, Giuseppe;CHIASELOTTI, Giampiero
2002-01-01
Abstract
Let $a_1,\ldots,a_n$ be $n$ real numbers with non negative sum. We showthat if $n\ge12$ there exist at least $n-1\choose 2$ subsets of$\{a_1,\ldots,a_n\}$ with three elements which have non--negative sum.File in questo prodotto:
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