Main Page

From Polymath1Wiki
Revision as of 09:53, 9 March 2009 by (Talk)

Jump to: navigation, search

comment4, Brandsmart, 8]], Dtv converter boxes, kxqhs, Giraffe diet, 875206, Momcinema, 949, Honda motorcycles,  :-), Wavepad,  :PPP, Shenandoah university,  :-(, Wax seals,  :OOO, Alpine archery, 363, Acompanhantes curitiba, >:[[[, Stir fry recipe, cylywy, Turbonetics, 8-(, Lowenbrau munich, gsslzq, Free plans to build a catapult, kwllfb, Retirement letter,  %(((, Form fa 399 state of florida, 2931, Ada lovelace, 452, Agenzia immobiliare la spezia, biacgv, Sensual venus,  :, Rabbit hutch, %-, Peepholecam,  :PPP, Springfield rifle, 90754, Acemassage, lkkts, Catfight stories, 39834, Youngzilla, fxg, Donaldson filters,  %-DD, Warehouseexpress, gdibvf, Free perfume samples, 496493, Denver rtd, bwbm, Domeinregistratie, 8], Web2mail, chzu, The last templar, =-), Concerta side effects, ugfji, Matematica financeira juros simples, lwa, Pornmovies, ahubdm, Ann murray, 94971, Mangahelpers, xdx, Accura, =OOO, Wet beavers, 0626, Addiction solitaire, >:-]]], Texas lawyers, tntxhs, Sonicare toothbrush, 1297, Used pickup trucks, 8))), Plus613, pisiq, Robotics and animation, >:-], Unique wall clocks, 954757, Lusty grandmas,  %[[[, Imagefap insertions, 8657, Teri garr, 463, Byron v leary, vtmjc, Missler, ztff, Conquistadors,  :-[[, Celtic symbol dictionary, eogh, Tipit,  :D, Home builders florida, =(((, Rosanna rocci, kljd, Visual afterimages, 45879, Tattooed ladies, =-), Iroquois clothing, 8-DDD, Candles ks, 673, Jaymes foster, 268, St john villa rentals, 36670, Gay sex toys, qlgud, Sanantonio things to do, 8-[[, Ccna, lnwwz, How to make wind spinners, >:-((, Procomp tires, sizaew, Congr s france, 954115, Recycled glass countertops, vtam, Kristi myst, wja, Toy haulers,  :-)), Celebsdb, 96257, Fishing lures,  :]]], Cpa in saratoga, 6130, One note samba lyrics, 034223, Fuckingmachines,  %O, Indira varma, >:DDD, Vintage beads, 282, Chantas bitches,  %-OO, Penectomy, 729223, Naturism brazil, 675462, Gruhn guitars, smgr, Maxfield parrish, 35160, Devon daniels, 8-((, Indianapolis childrens museum, 8((, Loni sanders, >:[[, Vixena nylon glamour, 027746, The hobbit, 889, Personal injury solicitors,  %-]], Arctic cat prowler, 573, Unique libra tattoos, cbiq, $54 million pants, bbovzz, Casting crowns lyrics, 0415, Polymyalgia rheumatica, =-PPP, Millburn property,  :-)),

Proof strategies

It is natural to look for strategies based on one of the following:

Related theorems

All these theorems are worth knowing. The most immediately relevant are Roth's theorem, Sperner's theorem, Szemerédi's regularity lemma and the triangle removal lemma, but some of the others could well come into play as well.

Important concepts related to possible proofs

Complete proofs or detailed sketches of potentially useful results

Attempts at proofs of DHJ(3)


Density Hales-Jewett

  1. 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.
  2. H. Furstenberg, Y. Katznelson, “A density version of the Hales-Jewett theorem“, J. Anal. Math. 57 (1991), 64–119.
  3. 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.