Monochromatic Schur triples in randomly perturbed dense sets of integers

Elad Aigner-Horev, Yury Person

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Given a dense subset A of the first n positive integers, we provide a short proof showing that for p = ω(n-2/3), the so-called randomly perturbed set A∩ [n]p a.a.s. has the property that any 2-coloring of it has a monochromatic Schur triple, i.e., a triple of the form (a, b, a + b). This result is optimal since there are dense sets A, for which A ∩ [n]p does not possess this property for p = o(n-2/3).

Original languageEnglish
Pages (from-to)2175-2180
Number of pages6
JournalSIAM Journal on Discrete Mathematics
Volume33
Issue number4
DOIs
StatePublished - 2019

Keywords

  • Ramsey theory
  • Random sets
  • Schur triples

Fingerprint

Dive into the research topics of 'Monochromatic Schur triples in randomly perturbed dense sets of integers'. Together they form a unique fingerprint.

Cite this