From Polymath1Wiki
Jump to: navigation, search

This is a (very partial) bibliography in density Ramsey theory and related topics. Additions to the bibliography are strongly encouraged!

Density Hales-Jewett

  1. T. Austin, Deducing the density Hales-Jewett theorem from an infinitary removal lemma, preprint.
  2. H. Furstenberg, Y. Katznelson, “A density version of the Hales-Jewett theorem for k = 3“, Graph Theory and Combinatorics (Cambridge, 1988). Discrete Math. 75 (1989), no. 1-3, 227–241. MR1001397
  3. H. Furstenberg, Y. Katznelson, “A density version of the Hales-Jewett theorem“, J. Anal. Math. 57 (1991), 64–119. MR1191743
  4. R. McCutcheon, “The conclusion of the proof of the density Hales-Jewett theorem for k=3“, unpublished.

Coloring Hales-Jewett theorem

  1. A. Hales, R. Jewett, Regularity and positional games, Trans. Amer. Math. Soc. 106 1963 222--229. MR143712
  2. N. Hindman, E. Tressler, "The first non-trivial Hales-Jewett number is four", preprint.
  3. P. Matet, "Shelah's proof of the Hales-Jewett theorem revisited", European J. Combin. 28 (2007), no. 6, 1742--1745. MR2339499
  4. S. Shelah, "Primitive recursive bounds for van der Waerden numbers", J. Amer. Math. Soc. 1 (1988), no. 3, 683--697. MR 929498

Roth's theorem

  1. E. Croot, "Szemeredi's theorem on three-term progressions, at a glance, preprint.

Behrend-type constructions

  1. M. Elkin, "An Improved Construction of Progression-Free Sets ", preprint.
  2. B. Green, J. Wolf, "A note on Elkin's improvement of Behrend's construction", preprint.
  3. K. O'Bryant, "Sets of integers that do not contain long arithmetic progressions", preprint.

Triangles and corners

  1. M. Ajtai, E. Szemerédi, Sets of lattice points that form no squares, Stud. Sci. Math. Hungar. 9 (1974), 9--11 (1975). MR369299
  2. I. Ruzsa, E. Szemerédi, Triple systems with no six points carrying three triangles. Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, pp. 939--945, Colloq. Math. Soc. János Bolyai, 18, North-Holland, Amsterdam-New York, 1978. MR519318
  3. J. Solymosi, A note on a question of Erdős and Graham, Combin. Probab. Comput. 13 (2004), no. 2, 263--267. MR 2047239

Kruskal-Katona theorem

  1. P. Keevash, "Shadows and intersections: stability and new proofs", preprint.

Moser's problem

  1. A. Chandra, On the solution of Moser's problem in four dimensions. Canad. Math. Bull. 16 (1973), 507--511.
  2. V. Chvatal, Remarks on a problem of Moser, Canadian Math Bulletin, Vol 15, 1972, 19-21.
  3. V. Chvatal, Edmonds polytopes and a hierarchy of combinatorial problems Discrete Math. 4 (1973) 305-337.
  4. Komlos, solution to problem P.170 by Leo Moser, Canad. Math.. Bull. vol (??check) (1972), 312-313, 1970.
  5. L. Moser, Problem P.170 in Canad. Math. Bull. 13 (1970), 268.

General texts

  1. R. Graham, B. Rothschild, J. Spencer, Ramsey theory, second edition, Wiley-Interscience, 1990