On Ramsey numbers for sets free of prescribed differences

Bruce M. Landman, James T. Perconti

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

For a positive integer d, a set S of positive integers is difference d-tree if \x-y\ # d for all x, y ε S. We consider the following Ramseytheoretical question: Given d, k, r ε Z+, what is the smallest integer n such that every r-coloring of [1, n] contains a monochromatic k-element difference d-free set? We provide a formula for this n. We then consider the more general problem where the monochromatic fc-element set must avoid a given set of differences rather than just one difference.

Original languageEnglish (US)
Pages (from-to)11-20
Number of pages10
JournalJournal of Combinatorial Mathematics and Combinatorial Computing
Volume76
StatePublished - Feb 1 2011
Externally publishedYes

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Keywords

  • Difference-free sets
  • Integer ramsey theory
  • Monochromatic sets

ASJC Scopus subject areas

  • Mathematics(all)

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