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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
GPpaper.ps
- Polynomial Extensions of VDW's and
Sz's thm, by
by Bergelson and Leibman.
Has the original proof of
Poly VDW thm.
BergLeib.pdf,
BergLeib.ps,
- Combinatorial Proofs of the
Poly VDW thm and the Poly HJ thm.
by Mark Walters.
This is the easier proof of Poly VDW.
walters.pdf,
walters.ps.
- Set-Polynomials and Polynomial Extensions
of the HJ thm.
by Bergelson and Leibman.
First proof of Poly-HJ. Hard.
polyHJ.pdf,
polyHJ.ps
- Two Combinatorial Theorems on Arithmetic Progressions
by Wolfgang Schmidt.
This gives some nice lower bounds on VDW numbers.
schmidtlowervdw.pdf,
schmidtlowervdw.ps.
- Monochromatic Equilateral Right Triangles
in the Integer Grid.
By Graham and Solymosi.
Gets a better upper bounds on W(3,c) as a corollary.
graham-solymosi.pdf,
graham-solymosi.ps.
- A New Method to Construct Lower Bounds for VDW Numbers.
By Herwig, Heule, Lamblagen, an Maaren.
lower-bds.pdf,
lower-bds.ps.
- On Sets of Integers Which Contain No Three Terms in
Arithmetic Progession.
By Salem and Spencer.
3ap-salem.pdf,
3ap-salem.ps,
- On Sets of Integers Not Containing Long Arithmetic Progressiosn.
By Laba and Lacey.
k-free-sets.pdf,
k-free-sets.ps
- A Restricted Version of HJ Thm.
By Deuber, Promel, Rothchild.
restrictedHJ.pdf,
restrictedHJ.ps
Other Generalizations and Variants of VDW
- Ramsey's Theorem for
-parameter sets.
by Graham and Rothchild.
A very general from which follows VDW and Ramsey.
Graham-Rothchild.pdf,
Graham-Rothchild.ps.
- Note on Combinatorial Analysis.
by Richard Rado's
This contains both Rado's thm and
Gallai-Witt thm
rado-gallai-german.pdf,
rado-gallai-german.ps,
or
rado-gallai-english.pdf,
rado-gallai-english.ps.
- Ein Kombinatorischer Satz der Elementgeometric (German)
By Von Ernst Witt.
Witt's article that contain Gallai-Witt thm.
witt.pdf,
witt.ps.
- An elementary proof of the canonizing version of Gallai-Witt's theorem
by Rödl and Prömel
CanGallaiWittElementary.pdf
My notes on this paper:
vdwcanNOTES.pdf,
vdwcanNOTES.ps
- A Canonical Partition Theorem for Equivalence Relations
on
. Deuber, Graham, Promel, Voigt.
VDWcan.pdf,
VDWcan.ps.
- Restricted Ramsey Configurations.
Spencer.
res-ram-config.pdf,
res-ram-config.ps
- VDW's thm on Homothetic Copies of
.
By Kim and Rho
VDWH.pdf,
VDWH.ps.
- Monochromatic Homothetic Copies of
.
VDWHcopies.pdf,
VDWHcopies.ps.
- APs in Sequences with Bounded Gaps,
by Tom Brown.
VDWgaps.pdf.
VDWgaps.ps,
- The 2-color relative linear VDW numbers. Kim and Rho
VDWlin.pdf.
VDWlin.ps,
- An Infinitary Polynomial VDW Thm.
By McCutcheon.
infinite-vdw.pdf,
infinite-vdw.ps
- Rainbow Arithmetic Progression and Anti-Ramsey Results.
By Jungic, Licht, Mahdian, Nesteril, Radoicic.
rainbow.pdf,
rainbow.ps
- Difference sets withouth squares.
by I.Z. Ruzsa
sqdiff-ruzsa.pdf,
sqdiff-ruzsa.ps.
Sz's Theorem
- Tau's exposition of Sz's thm
by Tau.
tauexpsz.pdf.
tauexpsz.ps,
- Notes on Sz's Reg Lemma
by Ernie Croot. Good exposition!
notesregularity.pdf,
notesregularity.ps.
- A New Proof of Sz's Thm for AP's of Length 4.
By Gowers.
gowers-sz-4AP.pdf,
gowers-sz-4AP.ps
- Roth's Thm on AP's.
By Iosevich.
notes-roth3ap.pdf,
notes-roth3ap.ps
- Sz Reg Lemma and its applications in Graph Theory.
By Komlos, Simonovitis.
szreg-applications.pdf,
szreg-applications.ps
- The Ergodic Theoretic Proof of Sz Thm.
By Furstenberg, Katznelson, Ornstein.
sz-thm-ergodic-easier.pdf,
sz-thm-ergodic-easier.ps
- A New Proof of Sz Thm.
By Gowers.
sz-thm-gowers-proof.pdf,
sz-thm-gowers-proof.ps
- An alternate proof
of Szemeredi's
cube lemma
using extremal
hypergraphs.
By Gunderson and
Rodl.
szcubedensity.pdf,
szcubedensity.ps.
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William Gasarch
2008-06-17