The maximum number of balancing sets

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1 Citation (Scopus)


Let a1, ..., an be a sequence of nonzero real numbers with sum zero. A subset B of {1, 2,..., n} is called a balancing set if ∑ ab = 0 (b ∈ B). S. Nabeya showed that the number of balancing sets is bounded above by {Mathematical expression} and this bound achieved for n even with aj =(-1)j. Here his conjecture is verified, showing a tight upper bound {Mathematical expression} when n = 2k + 1. The essentially unique extremal configuration is:a1 = 2, a2 = ... =ak = 1, ak+1 = ... =a2k+1 = -1.

Original languageEnglish
Pages (from-to)251-254
Number of pages4
JournalGraphs and Combinatorics
Issue number1
Publication statusPublished - Dec 1 1987

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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