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Monochromatic paths for the integers

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2016Embargo end date: 01 Jan 2016 Hungary English Publisher:Elsevier BVJournal:European Journal of Combinatorics, volume 58, pages 283-288 (issn: 0195-6698, Copyright policy )Funded by:EC | REGULARITY
Authors: João Guerreiro 0002; Imre Z. Ruzsa; Manuel Silva 0003;

doi: 10.1016/j.ejc.2016.06.002 , 10.48550/arxiv.1606.00418

arXiv: 1606.00418

Monochromatic paths for the integers

Abstract

Recall that van der Waerden's theorem states that any finite coloring of the naturals has arbitrarily long monochromatic arithmetic sequences. We explore questions about the set of differences of those sequences.

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Hungary
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Keywords

Permutations, words, matrices, QA Mathematics / matematika, Other combinatorial number theory, Ramsey theory, monochromatic arithmetic sequences, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 3
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green
hybrid
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