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V. Bergelson and A. Leibman.
Polynomial extensions of van der Waerden's and Szemerédi's
theorems.
Journal of the American Mathematical Society, pages 725-753,
1996.
http://www.math.ohio-state.edu/~vitaly/ or
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 2
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V. Bergelson and A. Leibman.
Set-polynomials and polynomial extension of the Hales-Jewett
theorem.
Annals of Mathematics, 150:33-75, 1999.
http://www.math.ohio-state.edu/~vitaly/ or
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 3
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E. Berlekamp.
A construction for partitions which avoids long arithmetic
progressions.
CMB, 11:409-414, 1968.
See www.cs.umd.edu/~gasarch//vdw/berlekampvdw.pdf.
- 4
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T. Brown and D. Hare.
Arithmetic progressions in sequence with bounded gaps.
JCTA, 77:222-227, 1997.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 5
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T. Brown, B. Landman, and M. Mishna.
Monochromatic homothetic copies of
.
CMB, 40:149-157, 1997.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 6
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W. Deuber, R. Graham, H. J. Prömel, and B. Voigt.
Canonical partition theorems for equivalence relations on
.
JCTA, 34(3):331-339, 1983.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 7
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W. Deuber, H. Prömel, B. Rothchild, and B. Voight.
A restricted version of Hales-Jewitt theorem.
In Finite and infinite sets, pages 231-246, 1983.
Also called Sixth Hungarian Combinatorial conference. See also
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 8
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H. Furstenberg.
Ergodic behavior of diagonal measures and a theorem of
Szemerédi's on arithmetic progressions.
Journal d'Analyse Mathematique, 31:204-256, 1977.
http://www.cs.umd.edu/~gasarch/vdw/furstenbergsz.pdf.
- 9
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R. Graham and B. Rothchild.
Ramsey's theorem for
-parameter sets.
Transactions of the American Mathematical Society, 159, 1971.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 10
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R. Graham and J. Solymosi.
Monochromatic equilateral right triangles on the integer grid.
Topics in Discrete Mathematics, Algorithms and Combinatorics,
2006.
www.math.ucsd.edu/~/ron/06_03_righttriangles.pdf or
www.cs.umd.edu/~/vdw/graham-solymosi.pdf.
- 11
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S. Gunderson, Rodl.
Independent arithmetic progressions in clique-free graphs on the
natural numbers.
JCTA, 93:1-17, 2001.
- 12
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P. Herwig, M. Heule, P. van Lambalgen, and H. van Maaren.
A new method to construct lower bounds for van der Waerden numbers.
The Electronic Journal of Combinatorics, 14, 2007.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 13
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B. Kim and Y.Rho.
Van der waerden's theorem on homothetic copies of
,
2005.
http://arxiv.org/abs/math/041-382 or
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 14
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B. M. Kim and Y. Rho.
The 2-color relative linear van der Waerden numbers.
C.R. Acad. Sci Paris, 345:183-186, 2007.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 15
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I. Laba and M. T. Lacey.
On sets of integers not containing long arithmetic progressions,
2001.
arxiv.org/pdf/math.CO/0108155 or
www.math.ubc.ca/~ilaba/preprints or
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 16
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R. McCutcheon.
An infinitary polynomial van de Waerden theorem.
JCTA, 86:214-231, 1999.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 17
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H. J. Prömel and V. Prömel.
An elementary proof of the canonizing version of Gallai-Witt's
theorem.
JCTA, 42:144-149, 1986.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 18
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R. Rado.
Studien zur kombinatorik.
Mathematische Zeitschrift, pages 424-480, 1933.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 19
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R. Rado.
Notes on combinatorial analysis.
Proceedings of the London Mathematical Society, pages 122-160,
1943.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 20
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I. Ruzsa.
Difference sets without squares.
Periodica Mathematica Hungarica, pages 205-209, 1984.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 21
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R. Salem and D. Spencer.
On set of integers which contain no three in arithmetic progression.
Proc. of the National Academy of Science (USA), 28:561-563,
1942.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 22
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A. Sárközy.
On differences of sets of sequences of integers I.
Acta Math. Sci. Hung., 31:125-149, 1978.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 23
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W. Schmidt.
Two combinatorial theorems on arithmetic progressions.
DMJ, 29:129-140, 1962.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 24
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Shelah.
A partition theorem.
Scientiae Math Japonicae, pages 413-438, 2002.
- 25
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J. Spencer.
Canonical configurations.
JCTA, 34:325-330, 1983.
See http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 26
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Z. Szabo.
An application of Lovasz's local lemma-- a new lower bound on the
van der Waerden numbers.
Random Structures and Algorithms, 1, 1990.
Available at http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 27
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M. Walters.
Combinatorial proofs of the polynomial van der Waerden theorem and
the polynomial Hales-Jewett theorem.
Journal of the London Mathematical Society, 61:1-12, 2000.
http://jlms.oxfordjournals.org/cgi/reprint/61/1/1 or
http://jlms.oxfordjournals.org/ or or
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
- 28
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Witt.
Ein kombinatorischer satz de elementargeometrie.
Mathematische Nachrichten, pages 261-262, 1951.
http://www.cs.umd.edu/~gasarch/vdw/vdw.html.
William Gasarch
2009-11-11