On the minimum number of monochromatic generalized Schur triples

Thotsaporn Thanatipanonda, Elaine Wong

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The solution to the problem of finding the minimum number of monochromatic triples (x, y, x + ay) with a ≥ 2 being a fixed positive integer over any 2-coloring of [1, n] was conjectured by Butler, Costello, and Graham (2010) and Thanathipanonda (2009). We solve this problem using a method based on Datskovsky’s proof (2003) on the minimum number of monochromatic Schur triples (x, y, x + y). We do this by exploiting the combinatorial nature of the original proof and adapting it to the general problem.

Original languageEnglish
Article number#P2.20
JournalElectronic Journal of Combinatorics
Volume24
Issue number2
DOIs
StatePublished - May 5 2017
Externally publishedYes

Keywords

  • Optimization
  • Rado Equation
  • Ramsey Theory on Integers
  • Schur Triples

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