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(Threads and further problems)
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== Threads and further problems==
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comment4, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3215 Brandsmart,  8]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3016 Dtv converter boxes,  kxqhs, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3209 Giraffe diet,  875206, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3108 Momcinema,  949, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3253 Honda motorcycles,  :-), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3027 Wavepad,  :PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3081 Shenandoah university,  :-(, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3053 Wax seals,  :OOO, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3083 Alpine archery,  363, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3170 Acompanhantes curitiba,  >:[[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3307 Stir fry recipe,  cylywy, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3239 Turbonetics,  8-(, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3117 Lowenbrau munich,  gsslzq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3229 Free plans to build a catapult,  kwllfb, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3286 Retirement letter,  %(((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3029 Form fa 399 state of florida,  2931, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3101 Ada lovelace,  452, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3160 Agenzia immobiliare la spezia,  biacgv, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3040 Sensual venus,  :[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3161 Rabbit hutch,  %-]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3100 Peepholecam,  :PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3272 Springfield rifle,  90754, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3275 Acemassage,  lkkts, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3304 Catfight stories,  39834, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3116 Youngzilla,  fxg, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3057 Donaldson filters,  %-DD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3223 Warehouseexpress,  gdibvf, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3284 Free perfume samples,  496493, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3132 Denver rtd,  bwbm, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3230 Domeinregistratie,  8], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3059 Web2mail,  chzu, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3300 The last templar,  =-), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3123 Concerta side effects,  ugfji, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3021 Matematica financeira juros simples,  lwa, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3267 Pornmovies,  ahubdm, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3061 Ann murray,  94971, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3054 Mangahelpers,  xdx, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3028 Accura,  =OOO, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3071 Wet beavers,  0626, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3256 Addiction solitaire,  >:-]]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3298 Texas lawyers,  tntxhs, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3148 Sonicare toothbrush,  1297, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3077 Used pickup trucks,  8))), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3138 Plus613,  pisiq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3026 Robotics and animation,  >:-], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3175 Unique wall clocks, 954757, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3097 Lusty grandmas,  %[[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3153 Imagefap insertions,  8657, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3109 Teri garr,  463, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3156 Byron v leary,  vtmjc, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3034 Missler,  ztff, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3261 Conquistadors,  :-[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3037 Celtic symbol dictionary,  eogh, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3165 Tipit,  :D, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3092 Home builders florida,  =(((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3084 Rosanna rocci,  kljd, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3237 Visual afterimages,  45879, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3201 Tattooed ladies,  =-), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3193 Iroquois clothing,  8-DDD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3078 Candles ks,  673, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3224 Jaymes foster,  268, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3154 St john villa rentals,  36670, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3287 Gay sex toys,  qlgud, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3187 Sanantonio things to do,  8-[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3232 Ccna,  lnwwz, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3159 How to make wind spinners,  >:-((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3280 Procomp tires,  sizaew, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3140 Congr s france,  954115, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3139 Recycled glass countertops,  vtam, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3226 Kristi myst,  wja, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3248 Toy haulers, :-)), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3271 Celebsdb,  96257, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3088 Fishing lures,  :]]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3130 Cpa in saratoga,  6130, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3278 One note samba lyrics,  034223, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3167 Fuckingmachines,  %O, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3228 Indira varma,  >:DDD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3135 Vintage beads,  282, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3015 Chantas bitches,  %-OO, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3012 Penectomy, 729223, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3194 Naturism brazil, 675462, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3192 Gruhn guitars,  smgr, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3060 Maxfield parrish,  35160, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3018 Devon daniels,  8-((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3288 Indianapolis childrens museum,  8((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3185 Loni sanders,  >:[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3013 Vixena nylon glamour,  027746, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3218 The hobbit,  889, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3225 Personal injury solicitors,  %-]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3141 Arctic cat prowler,  573, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3178 Unique libra tattoos,  cbiq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3126 $54 million pants,  bbovzz, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3205 Casting crowns lyrics,  0415, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3180 Polymyalgia rheumatica,  =-PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3279 Millburn property,  :-)),
 
+
* (1-199) [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/ A combinatorial approach to density Hales-Jewett] (inactive)
+
* (200-299) [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/ Upper and lower bounds for the density Hales-Jewett problem] (inactive)
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* (300-399) [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/ The triangle-removal approach] (inactive)
+
* (400-499) [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity Quasirandomness and obstructions to uniformity] (inactive)
+
* (500-599) [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#more-441/ Possible proof strategies] (inactive)
+
* (600-699) [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/ A reading seminar on density Hales-Jewett] (inactive)
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* (700-799) [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/ Bounds for the first few density Hales-Jewett numbers, and related quantities] (inactive)
+
* (800-849) [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/ Brief review of polymath1] (inactive)
+
* (850-899) [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/ DHJ(3): 851-899] (active)
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* (900-999) [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/ DHJ(3): 900-999 (Density Hales-Jewett type numbers)] (active)
+
 
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[http://blogsearch.google.com/blogsearch?hl=en&ie=UTF-8&q=polymath1&btnG=Search+Blogs Here is a further list of blog posts related to the Polymath1 project][http://en.wordpress.com/tag/polymath1/ Here is wordpress's list]. Here is a [[timeline]] of progress so far.
+
 
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A spreadsheet containing the latest upper and lower bounds for <math>c_n</math> can be found [http://spreadsheets.google.com/ccc?key=p5T0SktZY9DsU-uZ1tK7VEg here]Here are the proofs of our [[upper and lower bounds]] for these constants.
+
 
+
We are also collecting bounds for [[Fujimura's problem]], motivated by a [[hyper-optimistic conjecture]].
+
 
+
There is also a chance that we will be able to improve the known bounds on [[Moser's cube problem]].
+
 
+
Here are some [[unsolved problems]] arising from the above threads.
+
 
+
Here is a [[tidy problem page]].
+
  
 
== Proof strategies ==
 
== Proof strategies ==

Revision as of 08:53, 9 March 2009

comment4, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3215 Brandsmart, 8]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3016 Dtv converter boxes, kxqhs, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3209 Giraffe diet, 875206, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3108 Momcinema, 949, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3253 Honda motorcycles,  :-), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3027 Wavepad,  :PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3081 Shenandoah university,  :-(, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3053 Wax seals,  :OOO, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3083 Alpine archery, 363, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3170 Acompanhantes curitiba, >:[[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3307 Stir fry recipe, cylywy, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3239 Turbonetics, 8-(, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3117 Lowenbrau munich, gsslzq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3229 Free plans to build a catapult, kwllfb, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3286 Retirement letter,  %(((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3029 Form fa 399 state of florida, 2931, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3101 Ada lovelace, 452, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3160 Agenzia immobiliare la spezia, biacgv, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3040 Sensual venus,  :, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3161 Rabbit hutch, %-, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3100 Peepholecam,  :PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3272 Springfield rifle, 90754, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3275 Acemassage, lkkts, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3304 Catfight stories, 39834, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3116 Youngzilla, fxg, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3057 Donaldson filters,  %-DD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3223 Warehouseexpress, gdibvf, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3284 Free perfume samples, 496493, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3132 Denver rtd, bwbm, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3230 Domeinregistratie, 8], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3059 Web2mail, chzu, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3300 The last templar, =-), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3123 Concerta side effects, ugfji, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3021 Matematica financeira juros simples, lwa, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3267 Pornmovies, ahubdm, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3061 Ann murray, 94971, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3054 Mangahelpers, xdx, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3028 Accura, =OOO, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3071 Wet beavers, 0626, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3256 Addiction solitaire, >:-]]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3298 Texas lawyers, tntxhs, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3148 Sonicare toothbrush, 1297, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3077 Used pickup trucks, 8))), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3138 Plus613, pisiq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3026 Robotics and animation, >:-], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3175 Unique wall clocks, 954757, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3097 Lusty grandmas,  %[[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3153 Imagefap insertions, 8657, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3109 Teri garr, 463, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3156 Byron v leary, vtmjc, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3034 Missler, ztff, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3261 Conquistadors,  :-[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3037 Celtic symbol dictionary, eogh, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3165 Tipit,  :D, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3092 Home builders florida, =(((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3084 Rosanna rocci, kljd, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3237 Visual afterimages, 45879, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3201 Tattooed ladies, =-), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3193 Iroquois clothing, 8-DDD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3078 Candles ks, 673, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3224 Jaymes foster, 268, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3154 St john villa rentals, 36670, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3287 Gay sex toys, qlgud, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3187 Sanantonio things to do, 8-[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3232 Ccna, lnwwz, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3159 How to make wind spinners, >:-((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3280 Procomp tires, sizaew, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3140 Congr s france, 954115, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3139 Recycled glass countertops, vtam, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3226 Kristi myst, wja, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3248 Toy haulers,  :-)), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3271 Celebsdb, 96257, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3088 Fishing lures,  :]]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3130 Cpa in saratoga, 6130, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3278 One note samba lyrics, 034223, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3167 Fuckingmachines,  %O, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3228 Indira varma, >:DDD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3135 Vintage beads, 282, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3015 Chantas bitches,  %-OO, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3012 Penectomy, 729223, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3194 Naturism brazil, 675462, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3192 Gruhn guitars, smgr, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3060 Maxfield parrish, 35160, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3018 Devon daniels, 8-((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3288 Indianapolis childrens museum, 8((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3185 Loni sanders, >:[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3013 Vixena nylon glamour, 027746, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3218 The hobbit, 889, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3225 Personal injury solicitors,  %-]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3141 Arctic cat prowler, 573, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3178 Unique libra tattoos, cbiq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3126 $54 million pants, bbovzz, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3205 Casting crowns lyrics, 0415, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3180 Polymyalgia rheumatica, =-PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=3279 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)

Bibliography

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.