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Journal of the London Mathematical Society 2000 61(1):1-12; doi:10.1112/S0024610799008388
© 2000 by London Mathematical Society
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© The London Mathematical Society

Combinatorial Proofs of the Polynomial van der Waerden Theorem and the Polynomial Hales–Jewett Theorem

Mark Walters

Department of Pure Mathematics and Mathematical Statistics, Cambridge University 16 Mill Lane, Cambridge CB2 1SB, UK

Received 5 July 1998.

Recently Bergelson and Leibman proved an extension to van der Waerden's theorem involving polynomials. They also generalised the Hales–Jewett theorem in a similar way. The paper presents short and purely combinatorial proofs of those results.


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