Maximizing the number of nonnegative subsets

Noga Alon, Harout Aydinian, Hao Huang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Given a set of n real numbers, if the sum of the elements of every subset of size larger than k is negative, what is the maximum number of subsets of nonnegative sum? In this note we show that the answer is (n-1/k-1) + (n-1/k-2) + • • • + (n-1 0 )+ 1, settling a problem of Tsukerman. We provide two proofs; the first establishes and applies a weighted version of Hall's theorem, and the second is based on an extension of the nonuniform Erd.os-Ko-Rado theorem.

Original languageEnglish (US)
Pages (from-to)811-816
Number of pages6
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Erdos-Ko-Rado
  • Hall's theorem
  • Nonnegative subsets


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