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A WebPage on Van Der Waerden's Theorem
by William Gasarch
(For now this is just papers that I want to gather in one place)
VDW, poly-VDW, HJ, poly-HJ
- Draft of a book on VDW material by
Gasarch and Parrish
GPpaper.pdf
Purely Combinatorial.
- Polynomial Extensions of VDW's and
Sz's thm, by
by Bergelson and Leibman[1].
Has the original proof of
Poly VDW thm.
BergLeib.pdf,
Ergodic Methods.
- Combinatorial Proofs of the
Poly VDW thm and the Poly HJ thm.
by Mark Walters[26].
This is the easier proof of Poly VDW.
walters.pdf,
Purely Combinatorial.
- A Partition Theorem by Shelah[23].
polyvdwshelah.pdf
- Set-Polynomials and Polynomial Extensions
of the HJ thm.
by Bergelson and Leibman[2].
First proof of Poly-HJ. Hard.
polyHJ.pdf,
Ergodic Theory.
- Two Combinatorial Theorems on Arithmetic Progressions
by Wolfgang Schmidt[22].
This gives some nice lower bounds on VDW numbers.
schmidtlowervdw.pdf,
Purely combinatorial.
- Monochromatic Equilateral Right Triangles
in the Integer Grid.
By Graham and Solymosi[10].
Gets a better upper bounds on W(3,c) as a corollary.
graham-solymosi.pdf,
Purely combinatorial.
- A New Method to Construct Lower Bounds for VDW Numbers.
By Herwig, Heule, Lamblagen, an Maaren[11].
lower-bds.pdf,
Purely Combinatorial.
- On Sets of Integers Which Contain No Three Terms in
Arithmetic Progession.
By Salem and Spencer[20].
3ap-salem.pdf,
Purely Combinatorial.
- On Sets of Integers Not Containing Long Arithmetic Progressiosn.
By Laba and Lacey[14].
k-free-sets.pdf,
Purely Combinatorial.
- A Restricted Version of HJ Thm.
By Deuber, Promel, Rothchild[7].
restrictedHJ.pdf,
- An Application of Lovasz Local Lemma-- A New Lower Bound
for the van der Waerden Number [25].
by Soltan Szabo.
SZABOLOWER.PDF,
- A construction for partitions which avoid
long arithmetic progressions [3]
by E. Berlekamp.
BERLEKAMPVDW.PDF,
Other Generalizations and Variants of VDW
- Ramsey's Theorem for
-parameter sets.
by Graham and Rothchild[9].
A very general from which follows VDW and Ramsey.
Graham-Rothchild.pdf,
Hard.
- Note on Combinatorial Analysis.
by Richard Rado's
This contains both Rado's thm and
Gallai-Witt thm.
There is both a German version [17] and
an English version [18].
rado-gallai-german.pdf,
or
rado-gallai-english.pdf,
Purely Combinatorial.
- Ein Kombinatorischer Satz der Elementgeometric (German)
By Von Ernst Witt[27].
Witt's article that contain Gallai-Witt thm.
witt.pdf,
Purely Combinatorial but in German.
- An elementary proof of the canonizing version of Gallai-Witt's theorem
by Rödl and Prömel[16].
CanGallaiWittElementary.pdf
My notes on this paper:
vdwcanNOTES.pdf,
Purely Combinatorial.
- A Canonical Partition Theorem for Equivalence Relations
on
. Deuber, Graham, Promel, Voigt[6].
VDWcan.pdf,
Ergodic theorey or other hard techniques.
- Restricted Ramsey Configurations.
Spencer[24].
res-ram-config.pdf,
Purely Combinatorial.
- VDW's thm on Homothetic Copies of
.
By Kim and Rho [12].
VDWH.pdf,
- Monochromatic Homothetic Copies of
[5].
VDWHcopies.pdf,
- APs in Sequences with Bounded Gaps,
by Tom Brown and Donavan Hare[4].
VDWgaps.pdf.
- The 2-color relative linear VDW numbers by Kim and Rho[13].
VDWlin.pdf.
- An Infinitary Polynomial VDW Thm.
By McCutcheon[15].
infinite-vdw.pdf,
- Rainbow Arithmetic Progression and Anti-Ramsey Results.
By Jungic, Licht, Mahdian, Nesteril, Radoicic.
rainbow.pdf,
- Difference sets without squares.
by I.Z. Ruzsa[19].
sqdiff-ruzsa.pdf,
- On differences of sets of sequences of integers I [21]
by Sarkozy.
SARKOZYONE.PDF,
Sz's Theorem
- Tau's exposition of Sz's thm
by Tau.
tauexpsz.pdf.
- Notes on Sz's Reg Lemma
by Ernie Croot. Good exposition!
notesregularity.pdf,
- A New Proof of Sz's Thm for AP's of Length 4.
By Gowers.
gowers-sz-4AP.pdf,
- Roth's Thm on AP's.
By Iosevich.
notes-roth3ap.pdf,
- Sz Reg Lemma and its applications in Graph Theory.
By Komlos, Simonovitis.
szreg-applications.pdf,
- Ergodic behaviour of diagonal measures and a theorem of Szemerédi on arithmetic progressions [8]
by
Hillel Furstenberg.
FURSTENBERGSZ.PDF,
- The Ergodic Theoretic Proof of Sz Thm.
By Furstenberg, Katznelson, Ornstein.
sz-thm-ergodic-easier.pdf,
- A New Proof of Sz Thm.
By Gowers.
sz-thm-gowers-proof.pdf,
- An alternate proof
of Szemeredi's
cube lemma
using extremal
hypergraphs.
By Gunderson and
Rodl.
szcubedensity.pdf,
Next: Bibliography
William Gasarch
2009-11-02