A note on weak Sidon sequences

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Abstract

A sequence (ai) of integers is weak Sidon or well-spread if the sums ai+aj, for i<j, are all different. Let f(N) denote the maximum integer n for which there exists a weak Sidon sequence 0≤a1<⋯<an≤N. Using an idea of Lindström [An inequality for B2-sequences, J. Combin. Theory 6 (1969) 211-212], we offer an alternate proof that f(N)<N1/2+O(N1/4), an inequality due to Ruzsa [Solving a linear equation in a set of integers I, Acta. Arith. 65 (1993) 259-283]. The present proof improves Ruzsa's bound by decreasing the implicit constant, essentially from 4 to 3.

Original languageEnglish
Pages (from-to)141-144
Number of pages4
JournalDiscrete Mathematics
Volume299
Issue number1-3
DOIs
StatePublished - Aug 28 2005

Keywords

  • Weak Sidon
  • Well-spread

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