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Combinatorial Proofs of the Polynomial van der Waerden Theorem and the Polynomial Hales–Jewett Theorem
Author(s) -
Walters Mark
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008388
Subject(s) - van der waerden's theorem , mathematical proof , mathematics , combinatorics , combinatorial proof , proofs of fermat's little theorem , ramsey theory , extension (predicate logic) , polynomial , discrete mathematics , fundamental theorem , compactness theorem , computer science , mathematical analysis , fixed point theorem , geometry , programming language
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.