### Abstract

An increasing sequence of reals cursive Greek chi = 〈cursive Greek chi_{i}: i <ω〉 is simple if all "gaps" cursive Greek chi_{i+1}-cursive Greek chi_{i} are different. Two simple sequences cursive Greek chi and y are distance similar if cursive Greek chi_{i+1} - cursive Greek chi_{i} <cursive Greek chi_{j+1} - cursive Greek chi_{j} if and only if y_{i+1} - y_{i} <y_{j+1} - y_{j} 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 language | English |
---|---|

Pages (from-to) | 283-295 |

Number of pages | 13 |

Journal | Israel Journal of Mathematics |

Volume | 102 |

Publication status | Published - 1997 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Israel Journal of Mathematics*,

*102*, 283-295.

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

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 102, pp. 283-295.

}

TY - JOUR

T1 - On a metric generalization of ramsey's theorem

AU - Erdős, P.

AU - Hajnal, A.

AU - Pach, J.

PY - 1997

Y1 - 1997

N2 - 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 j+1 - cursive Greek chij if and only if yi+1 - yi j+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.

AB - 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 j+1 - cursive Greek chij if and only if yi+1 - yi j+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.

UR - http://www.scopus.com/inward/record.url?scp=0031527706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031527706&partnerID=8YFLogxK

M3 - Article

VL - 102

SP - 283

EP - 295

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -