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

1. Draft of a book on VDW material by Gasarch and Parrish GPpaper.pdf GPpaper.ps

2. 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,

3. 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.

4. Set-Polynomials and Polynomial Extensions of the HJ thm. by Bergelson and Leibman. First proof of Poly-HJ. Hard. polyHJ.pdf, polyHJ.ps

5. Two Combinatorial Theorems on Arithmetic Progressions by Wolfgang Schmidt. This gives some nice lower bounds on VDW numbers. schmidtlowervdw.pdf, schmidtlowervdw.ps.

6. 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.

7. A New Method to Construct Lower Bounds for VDW Numbers. By Herwig, Heule, Lamblagen, an Maaren. lower-bds.pdf, lower-bds.ps.

8. On Sets of Integers Which Contain No Three Terms in Arithmetic Progession. By Salem and Spencer. 3ap-salem.pdf, 3ap-salem.ps,

9. On Sets of Integers Not Containing Long Arithmetic Progressiosn. By Laba and Lacey. k-free-sets.pdf, k-free-sets.ps

10. A Restricted Version of HJ Thm. By Deuber, Promel, Rothchild. restrictedHJ.pdf, restrictedHJ.ps

Other Generalizations and Variants of VDW

1. Ramsey's Theorem for $n$-parameter sets. by Graham and Rothchild. A very general from which follows VDW and Ramsey. Graham-Rothchild.pdf, Graham-Rothchild.ps.

2. 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.

3. Ein Kombinatorischer Satz der Elementgeometric (German) By Von Ernst Witt. Witt's article that contain Gallai-Witt thm. witt.pdf, witt.ps.

4. 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

5. A Canonical Partition Theorem for Equivalence Relations on $Z^n$. Deuber, Graham, Promel, Voigt. VDWcan.pdf, VDWcan.ps.

6. Restricted Ramsey Configurations. Spencer. res-ram-config.pdf, res-ram-config.ps

7. VDW's thm on Homothetic Copies of $\{1,1+s,1+s+t\}$. By Kim and Rho VDWH.pdf, VDWH.ps.

8. Monochromatic Homothetic Copies of $\{1,1+s,1+s+t\}$. VDWHcopies.pdf, VDWHcopies.ps.

9. APs in Sequences with Bounded Gaps, by Tom Brown. VDWgaps.pdf. VDWgaps.ps,

10. The 2-color relative linear VDW numbers. Kim and Rho VDWlin.pdf. VDWlin.ps,

11. An Infinitary Polynomial VDW Thm. By McCutcheon. infinite-vdw.pdf, infinite-vdw.ps

12. Rainbow Arithmetic Progression and Anti-Ramsey Results. By Jungic, Licht, Mahdian, Nesteril, Radoicic. rainbow.pdf, rainbow.ps

13. Difference sets withouth squares. by I.Z. Ruzsa sqdiff-ruzsa.pdf, sqdiff-ruzsa.ps.

Sz's Theorem

1. Tau's exposition of Sz's thm by Tau. tauexpsz.pdf. tauexpsz.ps,

2. Notes on Sz's Reg Lemma by Ernie Croot. Good exposition! notesregularity.pdf, notesregularity.ps.

3. A New Proof of Sz's Thm for AP's of Length 4. By Gowers. gowers-sz-4AP.pdf, gowers-sz-4AP.ps

4. Roth's Thm on AP's. By Iosevich. notes-roth3ap.pdf, notes-roth3ap.ps

5. Sz Reg Lemma and its applications in Graph Theory. By Komlos, Simonovitis. szreg-applications.pdf, szreg-applications.ps

6. The Ergodic Theoretic Proof of Sz Thm. By Furstenberg, Katznelson, Ornstein. sz-thm-ergodic-easier.pdf, sz-thm-ergodic-easier.ps

7. A New Proof of Sz Thm. By Gowers. sz-thm-gowers-proof.pdf, sz-thm-gowers-proof.ps

8. An alternate proof of Szemeredi's cube lemma using extremal hypergraphs. By Gunderson and Rodl. szcubedensity.pdf, szcubedensity.ps.