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Abstract

We give simple randomized algorithms leading to new upper bounds for combinatorial problems of Choi and Erdös: For an arbitrary additive group G let P n (G) denote the set of all subsets S of G with n elements having the property that 0 is not in S + S. Call a subset A of G admissible with respect to a set S from P n (G) if the sum of each pair of distinct elements of A lies outside S. For SP n (G) let h(S) denote the maximal cardinality of a subset of S admissible with respect to S. In particular we show \(h(n) := \mathrm{min}\{h(S) \vert G \mathrm{group}, S \in P_n(G)\} = \mathcal{O}((\ln n)^2)\). The methodical innovation of the whole approach is the use of large Sidon sets.

Keywords

Strongly Sum-Free Sets Sidon Sets Independent Sets in Hypergraphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Andreas Baltz
    • 1
  • Tomasz Schoen
    • 1
  • Anand Srivastav
    • 1
  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany

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