On a metric generalization of ramsey's theorem

P. Erdős, A. Hajnal, J. Pach

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

An increasing sequence of reals cursive Greek chi = 〈cursive Greek chii: i <ω〉 is simple if all "gaps" cursive Greek chii+1-cursive Greek chii are different. Two simple sequences cursive Greek chi and y are distance similar if cursive Greek chii+1 - cursive Greek chii <cursive Greek chij+1 - cursive Greek chij if and only if yi+1 - yi <yj+1 - yj for all i and j. Given any bounded simple sequence cursive Greek chi and any coloring of the pairs of rational numbers by a finite number of colors, we prove that there is a sequence y distance similar to cursive Greek chi all of whose pairs are of the same color. We also consider many related problems and generalizations.

Original languageEnglish
Pages (from-to)283-295
Number of pages13
JournalIsrael Journal of Mathematics
Volume102
Publication statusPublished - 1997

Fingerprint

Ramsey's Theorem
Metric
Monotonic increasing sequence
Colouring
If and only if
Generalization
Color

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On a metric generalization of ramsey's theorem. / Erdős, P.; Hajnal, A.; Pach, J.

In: Israel Journal of Mathematics, Vol. 102, 1997, p. 283-295.

Research output: Contribution to journalArticle

Erdős, P, Hajnal, A & Pach, J 1997, 'On a metric generalization of ramsey's theorem', Israel Journal of Mathematics, vol. 102, pp. 283-295.
Erdős, P. ; Hajnal, A. ; Pach, J. / On a metric generalization of ramsey's theorem. In: Israel Journal of Mathematics. 1997 ; Vol. 102. pp. 283-295.
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