Published August 20, 2019
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Intervals in the Hales-Jewett theorem
- Creators
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Conlon, David
- Kamčev, Nina
Abstract
The Hales-Jewett theorem states that for any m and r there exists an n such that any r-colouring of the elements of [m]^n contains a monochromatic combinatorial line. We study the structure of the wildcard set S ⊆ [n] which determines this monochromatic line, showing that when r is odd there are r-colourings of [3]^n where the wildcard set of a monochromatic line cannot be the union of fewer than r intervals. This is tight, as for n sufficiently large there are always monochromatic lines whose wildcard set is the union of at most r intervals.
Additional Information
Conlon research supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. The second author would like to thank Sarah Gales, Hannah and Sven Eggimann for hosting her in Oxford while this research was conducted. We would also like to thank the anonymous referee for a number of helpful remarks.Attached Files
Submitted - 1801.08919.pdf
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Additional details
- Eprint ID
- 98026
- Resolver ID
- CaltechAUTHORS:20190819-170911002
- Royal Society
- 676632
- European Research Council (ERC)
- Created
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2019-08-20Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field