Sumsets with distinct summands and the Erdõs-Heilbronn conjecture on sums of residues

Gregory A. Freiman*, Lewis Low, Jane Pitman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let S be a set of integers or of residue classes modulo a prime p, with cardinality |S| = k, and let T be the set of all sums of two distinct elements of S. For the integer case, it is shown that if |T| is less than approximately 2.5k then S is contained in an arithmetic progression with relatively small cardinality. For the residue class case a result of this type is derived provided that k > 60 and p > 50k. As an application, it is shown that |T| ≥ 2k-3 under these conditions. Earlier results of Freiman play an essential role in the proofs.

Original languageEnglish
Pages (from-to)163-172
Number of pages10
JournalAsterisque
Volume258
StatePublished - 1999

Keywords

  • Set addition
  • Sums of residues
  • Sumset

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