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Integer Sets Containing No Arithmetic Progressions
Abstract
lfh and k are positive integers there exists N(h, k) such that whenever N ^ N(h, k), and the integers 1,2,...,N are divided into h subsets, at least one must contain an arithmetic progression of length k. This is the famous theorem of van der Waerden [10], dating from 1927. The proof of this uses multiple nested inductions, which result
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Cited by
A New Proof of Szemer�di's Theorem for Arithmetic Progressions of Length Four
Gowers, W. T. (1998) · Geometric And Functional Analysis · doi:10.1007/s000390050065 · Cited by 417
New applications of the polynomial method: The cap set conjecture and beyond
Grochow, J. (2018) · Bulletin of the American Mathematical Society · doi:10.1090/bull/1648 · Cited by 16
Metadata
- Authors
- Heath-Brown, D. R.
- Venue
- Journal of the London Mathematical Society
- Publisher
- Wiley
- Published
- 1987-06
- Volume
- s2-35
- Issue
- 3
- Pages
- 385-394
- ISSN
- 0024-6107 (ISSN-L)
- OpenAlex
- W2041824078
- Cited by
- 161
- References
- 0
- FWCI
- 1.58
- Type
- journal article
- Language
- en
- Open access
- closed
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- Heath-Brown, D. R. (1987). Integer Sets Containing No Arithmetic Progressions. Journal of the London Mathematical Society. https://doi.org/10.1112/jlms/s2-35.3.385
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
