A new proof of the density Hales-Jewett theorem

@article{Polymath2009ANP,
  title={A new proof of the density Hales-Jewett theorem},
  author={D. Polymath},
  journal={arXiv: Combinatorics},
  year={2009}
}
  • D. Polymath
  • Published 2009
  • Mathematics
  • arXiv: Combinatorics
The Hales-Jewett theorem asserts that for every r and every k there exists n such that every r-colouring of the n-dimensional grid {1,...,k}^n contains a combinatorial line. This result is a generalization of van der Waerden's theorem, and it is one of the fundamental results of Ramsey theory. The theorem of van der Waerden has a famous density version, conjectured by Erdos and Turan in 1936, proved by Szemeredi in 1975, and given a different proof by Furstenberg in 1977. The Hales-Jewett… Expand
102 Citations

Figures from this paper

Polymath and The Density Hales-Jewett Theorem
  • 5
Proof of the Brown–Erdős–Sós conjecture in groups
  • 4
A Probabilistic Technique for Finding Almost-Periods of Convolutions
  • 75
  • PDF
2 PANDELIS DODOS The Hales – Jewett
  • PDF
Density Hales-Jewett and Moser Numbers
  • 24
  • PDF
SOME RECENT RESULTS IN RAMSEY THEORY
  • 1
  • PDF
Density Hales-Jewett Theorem
  • 1
A short proof of the multidimensional Szemerédi theorem in the primes
  • 9
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 70 REFERENCES
A density version of the Hales-Jewett theorem for k=3
  • 31
  • PDF
Deducing the Density Hales–Jewett Theorem from an Infinitary Removal Lemma
  • 22
  • PDF
A Quantitative Ergodic Theory Proof of Szemerédi's Theorem
  • T. Tao
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 2006
  • 98
  • PDF
DENSITY HALES-JEWETT AND MOSER NUMBERS IN LOW DIMENSIONS
  • 1
  • PDF
A new proof of Szemerédi's theorem
  • 740
  • Highly Influential
  • PDF
Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs
  • W. T. Gowers
  • Mathematics, Computer Science
  • Combinatorics, Probability and Computing
  • 2006
  • 166
  • PDF
...
1
2
3
4
5
...