*Variations on a theorem by van der Waerden*
by Karen Johannson.
Masters Thesis.
HERE

*Variations on a theorem by van der Waerden*
by Sohail Farhangi.
Masters Thesis.
Focus on the set of naturals the difference can come from.
HERE

*Van der waerden's theorem: Variants and “Applications”*
Very Rough Draft of a book on VDW material by
Gasarch and Kruskal and Parrish
HERE

*Combinatorial Number Theory: Resuls of Hilbert, Schur, Folkman, and Hindman*
By Yudi Setyawan. Masters Degree
HERE

*Primitive recurive bounds on the VDW numbers* by Saharon Shelah.
HERE

*On sets of integers containing no for elements in arithmetic progression*
by Endre Szemeredi.
This has Szemeredi's Density theorem for k=4.
HERE

*Polynomial Extensions of VDW's and Sz's thm* by Bergelson and Leibmancite{pvdw}.
Has the original proof of Poly VDW thm.
Using Ergodic Methods.
HERE

*Combinatorial Proofs of the Poly VDW thm and the Poly HJ theorem* by Mark Walters
This has the elementary proof of Poly VDW.
HERE

*A Partition Theorem* by Shelah. Primitive Rec bounds on poly HJ so poly VDW. HERE

*Set-Polynomials and Polynomial Extensions of the HJ thm* by Bergelson and Leibman
First proof of Poly-HJ. Uses Ergodic Theory.
HERE

*Two Combinatorial Theorems on Arithmetic Progressions*
by Wolfgang Schmidtcite{twocomb}.
This gives some nice lower bounds on VDW numbers.
Purely combinatorial.
HERE

*Monochromatic Equilateral Right Triangles in the Integer Grid*
By Graham and Solymosi.
Gets a better upper bounds on W(3,c) as a corollary.
HERE

*A New Method to Construct Lower Bounds for VDW Numbers*
By Herwig, Heule, Lamblagen, an Maaren
Purely Combinatorial.
HERE

*The van der Waerden Number is 1132* By Michal Kouril and Jerome Paul.
HERE

*Investigating Monte-Carlo Methods on the Weak Schur Problem* by Eliahou, Fonlupt, Fromentin, Marion-Poty, Robilliard, Teytaud. They find n such that any 6-coloring of n has a mono x,y,z with x+y=z. HERE

*On Sets of Integers Which Contain No Three Terms in Arithmetic Progession*
By Salem and Spencer.
Purely Combinatorial.
HERE

*An improved construction of Progression-free sets* by Michael Elkin.
This paper improves Behrend result on large 3-free sts. Elementary.
HERE

*A note on Elkin's improvement of Behrend's Construction*
by Green and Wolfe.
A shorter proof of Elkin's result
HERE

*On Sets of Integers Not Containing Long Arithmetic Progressiosn* By Laba and Lacey Purely Combinatorial. HERE

*Large -free sets based on Elkin's improvement of Behrends* by Kevin O'Bryant. HERE

*A Restricted Version of HJ Thm* By Deuber, Promel, Rothschild. HERE

*An Application of Lovasz Local Lemma — A New Lower Bound for the van der Waerden Number* by Soltan Szabo. HERE

*A construction for partitions which avoid long arithmetic progressions*
by E. Berlekamp.
HERE

*Integer sets containing no arithmetic progressions* by Szemeredi HERE

*Integer sets containing no arithmetic progressions* by Heath-Brown HERE

*Triples in Arithmetic progression* by Bourgain. HERE

*Canonical Partition Theorems for parameter sets* by H.J. Promel and B.Voight.
They prove a very general canonical theorems.
One of the corollaries is Can Hales-Jewitt.
HERE

*A lower bound for off-diagonal van der Waerden numbers* by Yusheng Li and Jinlong Shu. HERE

*Extremal binary matrices without constant 2-squares* by Roland Batcher and Shalom Eliahou HERE In this paper they show that every 2-coloring of the 15 by 15 grid has a mono square.

*On Monochromatic subsets of a rectangular grid*
By Maria Axenovich and Jacob Manske.
They prove that any 2-coloring of VDW(8,2) by VDW(8,2) has a mono square.
HERE

*Searching for Monochromatic-Square-Free Ramsey Grid Colorings via SAT Solvers* By Paul Walton and Wing Ning Li. This paper also has a 2-coloring of without a mono square and shows you can't do 15. HERE

*Independent Arithmetic progressions in clique-free graphs on the natural numbers* by Gunderson, Rodl, Sidorenko. HERE

*Ramsey's Theorem for -parameter sets* by Graham and Rothschild.
A very general from which follows VDW and Ramsey.
HERE

*Note on Combinatorial Analysis* by Richard Rado.
This contains both Rado's thm and Gallai-Witt thm.
There is both a German version and
an English version cite{radoenglish}.
Purely Combinatorial.
German Version
English Version

*Ein Kombinatorischer Satz der Elementgeometric (German)*
By Von Ernst Wittcite{witt}.
Witt's article that contain Gallai-Witt thm.
Purely Combinatorial but in German.
HERE

*An ergodic Szemeredi Theorem for commuting transformations*
By Furstenberg and Katznelson cite{densityGW}.
This has a density version of the Gallai-Witt theorem.
HERE

*On Erdos-Rado Numbers*
By Lefmann and Rodl.
They get better bounds on Can Ramsey Numbers for Graphs.
HERE

*An elementary proof of the canonizing version of Gallai-Witt's theorem*
by R{"o}dl and Pr{"o}mel.
Purely Combinatorial.
HERE
My Notes on this paper

*A Canonical Partition Theorem for Equivalence Relations on Z^n*
by Deuber, Graham, Promel, Voigt.
Ergodic theorey or other hard techniques.
HERE

*Partition Theorems and Computability Theory*
by Joseph Mileti.
HERE

*Restricted Ramsey Configurations*
by Joel Spencer.
Purely Combinatorial.
HERE

*VDW's thm on Homothetic Copies of {1,1 s,1s+t}*
By Kim and Rho.
HERE

*Monochromatic Homothetic Copies of {1,1 s,1s+t}*
HERE

*APs in Sequences with Bounded Gaps*
by Tom Brown and Donavan Hare
HERE

*The 2-color relative linear VDW numbers* by Kim and Rho.
HERE

*An Infinitary Polynomial VDW Theorem*
By McCutcheon.
HERE

*Rainbow Arithmetic Progression and Anti-Ramsey Results*
By Jungic, Licht, Mahdian, Nesteril, Radoicic.
HERE

*Difference sets without squares*
by I.Z. Ruzsa.
HERE

*On differences of sets of sequences of integers I*
by Sarkozy.
HERE

*Sets whose differences set is square-free* by Julia Wolf.
HERE

*On sets of natural numbers whose difference set contains on squares*
By Pintz, Steiger, Szemeredi.
HERE

*On differences of sequences of integers III*
by Sarkozy
HERE

*Tau's exposition of Szemeredi's theorem*
by Tau.
HERE

*Notes on Sz's Reg Lemma*
by Ernie Croot. Good exposition!
HERE

*A New Proof of Sz's Thm for AP's of Length 4*
By Gowers.
HERE

*Roth's Thm on AP's* by Roth.
Roth's original paper
HERE
NOTE by Iosevich

*Sz Reg Lemma and its applications in Graph Theory*
By Komlos and Simonovitis.
HERE

*Ergodic behaviour of diagonal measures and a theorem of {S}zemer{'e}di on arithmetic progressions*
by Hillel Furstenberg.
HERE

*The Ergodic Theoretic Proof of Sz Thm* By Furstenberg, Katznelson, Ornstein.
HERE

*A New Proof of Sz Thm* By Gowers. HERE

*An alternate proof of Szemeredi's cube lemma using extremal hypergraphs*
By Gunderson and Rodl.
HERE