OKlibrary  0.2.1.6
Datak6.hpp File Reference

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 6 (length of arithmetic progressions) More...

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Detailed Description

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 6 (length of arithmetic progressions)

Todo:
Elementary statistics
  • Investigating tr_arithprog_hg(6,n).
  • The numbers of minimum hyperedges:
    L6 : [];
    minimum_transversals_decomp_gen(inf,lambda([n],arithprog_primes_hg(6,n)),'L6)$
    
    1 1 0 [0,1,1]
    37 37 1 [1,6,32]
    55 55 2 [2,36,45]
    64 64 3 [3,216,49]
    71 71 4 [4,1296,51]
    90 90 5 [5,7776,65]
    97 97 6 [6,46656,67]
    125 125 7 [7,279936,90]
    134 134 8 [7,93312,95]
    143 143 9 [7,15552,99]
    146 146 10 [7,5184,98]
    152 152 11 [8,31104,99]
    155 155 12 [8,15552,101]
    160 160 13 [8,7776,103]
    162 162 14 [9,46656,100]
    179 179 15 [10,699840,113]
    184 184 16 [10,116640,113]
    200 200 17 [10,19440,124]
    201 201 18 [11,184680,121]
    204 204 19 [12,1108080,119]
    211 211 20 [13,12188880,121]
    212 212 21 [14,109699920,119]
    214 214 22 [14,109699920,120]
    228 228 23 [14,98152560,133]
    232 232 24 [14,81793800,136]
    242 242 25 [14,13632300,141]
    250 250 26 [15,204484500,145]
    263 263 27 [15,163587600,157]
    269 269 28 [15,87246720,160]
    275 275 29 [15,15863040,163]
    289 289 30 [15,11897280,176]
    292 292 31 [16,130870080,174]
    293 293 32 [17,785220480,170]
    294 294 33 [17,232657920,167]
    307 307 34 [17,21150720,176]
    315 315 35 [18,444165120,180]
    316 316 36 [18,296110080,180]
    323 323 39 [19,1295481600,180]
    324 324 40 [19,161935200,177]
    327 327 41 [20,1214514000,175]
    329 329 42 [20,57834000,175]
    341 341 43 [21,636174000,182]
    349 349 44 [21,617997600,189]
    351 351 46 [22,617997600,181]
    352 352 47 [23,14831942400,179]
    357 357 48 [23,5234803200,179]
    358 358 49 [23,1385683200,176]
    360 360 50 [24,8314099200,173]
    368 368 51 [24,2267481600,178]
    374 374 52 [25,45349632000,180]
    383 383 53 [25,11337408000,186]
    396 396 55 [25,7558272000,198]
    408 408 56 [26,45489600000,205]
    413 413 57 [26,12636000000,206]
    424 424 58 [27,75816000000,212]
    428 428 59 [27,23166000000,213]
    432 432 60 [27,5274720000,215]
    435 435 61 [28,31648320000,213]
    440 440 62 [28,2109888000,213]
    444 444 63 [29,14577408000,212]
    455 455 64 [29,2429568000,218]
    469 469 65 [29,223776000,230]
    471 471 66 [30,5370624000,231]
    474 474 67 [30,537062400,231]
    476 476 68 [30,234964800,229]
    477 477 69 [30,33566400,226]
    479 479 70 [31,872726400,223]
    485 485 71 [31,498700800,225]
    487 487 72 [32,5485708800,222]
    506 506 73 [32,421977600,236]
    508 508 74 [32,210988800,234]
    517 517 76 [33,1245974400,238]
    519 519 77 [34,63544694400,235]
    520 520 79 [34,5295391200,229]
    526 526 80 [34,4776235200,232]
    539 539 81 [34,434203200,242]
    552 552 82 [35,3039422400,250]
    563 563 83 [35,111283200,257]
    570 570 84 [35,111283200,263]
    590 590 85 [36,5119027200,282]
    593 593 86 [37,312260659200,280]
    604 604 87 [37,33941376000,288]
    611 611 88 [38,719557171200,290]
    612 612 89 [39,4831312435200,286]
    617 617 90 [39,237605529600,288]
    630 630 91 [39,114319641600,299]
    641 641 93 [39,76213094400,309]
    643 643 95 [40,457278566400,301]
    647 647 96 [41,5487342796800,301]
    650 650 97 [42,73164570624000,299]
    653 653 98 [43,438987423744000,297]
    659 659 99 [43,242844106752000,300]
    661 661 100 [43,64758428467200,298]
    665 665 101 [43,64758428467200,301]
    666 666 102 [44,388550570803200,297]
    675 675 103 [45,4873775638118400,303]
    676 676 104 [45,2436887819059200,301]
    690 690 106 [45,1218443909529600,314]
    698 698 107 [45,152305488691200,318]
    703 703 108 [45,49499283824640,319]
    706 706 109 [45,22845823303680,319]
    710 710 110 [45,6980668231680,319]
    715 715 111 [45,3807637217280,323]
    728 728 112 [45,1903818608640,334]
    732 732 113 [46,24749641912320,333]
    736 736 114 [46,4124940318720,332]
    743 743 115 [46,2538424811520,336]
    744 744 116 [47,15230548869120,332]
    750 750 117 [48,167536037560320,333]
    754 754 118 [49,1415843768401920,333]
    755 755 119 [50,69730305593794560,329]
    756 756 120 [50,11621717598965760,325]
    770 770 121 [50,1051617137725440,335]
    778 778 122 [51,15774257065881600,339]
    779 779 123 [51,2629042844313600,337]
    781 781 124 [52,16785427390617600,334]
    783 783 125 [53,1712113593842995200,333]
    786 786 126 [53,112756181223628800,333]
    788 788 127 [53,15034157496483840,332]
    
    T : transform_steps_l(map(lambda([d],d[4][1]),reverse(L6)));
     [36,54,63,70,89,96,124,151,161,178,200,203,210,211,249,291,292,314,322,326,340,350,351,359,373,407,423,434,443,470,478,486,516,518,551,589,592,610,611,642,646,649,652,665,674,731,743,749,753,754,777,780,782]
    length(T);
     53
       
  • Due to the rather sparse nature of the hypergraphs, at least initially with a new hyperedge we get typically a factor of 6.
Todo:
Only computing the transversal numbers
  • Just computing the transversal numbers, using minisat2 and the direct translation (as provided by "GTTransversalsInc 6 1 0 OutputFile OutputSAT"):
    k n tau
    6 1 0
    6 2 0
    6 3 0
    6 4 0
    6 5 0
    6 6 0
    6 7 0
    6 8 0
    6 9 0
    6 10 0
    6 11 0
    6 12 0
    6 13 0
    6 14 0
    6 15 0
    6 16 0
    6 17 0
    6 18 0
    6 19 0
    6 20 0
    6 21 0
    6 22 0
    6 23 0
    6 24 0
    6 25 0
    6 26 0
    6 27 0
    6 28 0
    6 29 0
    6 30 0
    6 31 0
    6 32 0
    6 33 0
    6 34 0
    6 35 0
    6 36 0
    6 37 1
    6 38 1
    6 39 1
    6 40 1
    6 41 1
    6 42 1
    6 43 1
    6 44 1
    6 45 1
    6 46 1
    6 47 1
    6 48 1
    6 49 1
    6 50 1
    6 51 1
    6 52 1
    6 53 1
    6 54 1
    6 55 2
    6 56 2
    6 57 2
    6 58 2
    6 59 2
    6 60 2
    6 61 2
    6 62 2
    6 63 2
    6 64 3
    6 65 3
    6 66 3
    6 67 3
    6 68 3
    6 69 3
    6 70 3
    6 71 4
    6 72 4
    6 73 4
    6 74 4
    6 75 4
    6 76 4
    6 77 4
    6 78 4
    6 79 4
    6 80 4
    6 81 4
    6 82 4
    6 83 4
    6 84 4
    6 85 4
    6 86 4
    6 87 4
    6 88 4
    6 89 4
    6 90 5
    6 91 5
    6 92 5
    6 93 5
    6 94 5
    6 95 5
    6 96 5
    6 97 6
    6 98 6
    6 99 6
    6 100 6
    6 101 6
    6 102 6
    6 103 6
    6 104 6
    6 105 6
    6 106 6
    6 107 6
    6 108 6
    6 109 6
    6 110 6
    6 111 6
    6 112 6
    6 113 6
    6 114 6
    6 115 6
    6 116 6
    6 117 6
    6 118 6
    6 119 6
    6 120 6
    6 121 6
    6 122 6
    6 123 6
    6 124 6
    6 125 7
    6 126 7
    6 127 7
    6 128 7
    6 129 7
    6 130 7
    6 131 7
    6 132 7
    6 133 7
    6 134 7
    6 135 7
    6 136 7
    6 137 7
    6 138 7
    6 139 7
    6 140 7
    6 141 7
    6 142 7
    6 143 7
    6 144 7
    6 145 7
    6 146 7
    6 147 7
    6 148 7
    6 149 7
    6 150 7
    6 151 7
    6 152 8
    6 153 8
    6 154 8
    6 155 8
    6 156 8
    6 157 8
    6 158 8
    6 159 8
    6 160 8
    6 161 8
    6 162 9
    6 163 9
    6 164 9
    6 165 9
    6 166 9
    6 167 9
    6 168 9
    6 169 9
    6 170 9
    6 171 9
    6 172 9
    6 173 9
    6 174 9
    6 175 9
    6 176 9
    6 177 9
    6 178 9
    6 179 10
    6 180 10
    6 181 10
    6 182 10
    6 183 10
    6 184 10
    6 185 10
    6 186 10
    6 187 10
    6 188 10
    6 189 10
    6 190 10
    6 191 10
    6 192 10
    6 193 10
    6 194 10
    6 195 10
    6 196 10
    6 197 10
    6 198 10
    6 199 10
    6 200 10
    6 201 11
    6 202 11
    6 203 11
    6 204 12
    6 205 12
    6 206 12
    6 207 12
    6 208 12
    6 209 12
    6 210 12
    6 211 13
    6 212 14
    6 213 14
    6 214 14
    6 215 14
    6 216 14
    6 217 14
    6 218 14
    6 219 14
    6 220 14
    6 221 14
    6 222 14
    6 223 14
    6 224 14
    6 225 14
    6 226 14
    6 227 14
    6 228 14
    6 229 14
    6 230 14
    6 231 14
    6 232 14
    6 233 14
    6 234 14
    6 235 14
    6 236 14
    6 237 14
    6 238 14
    6 239 14
    6 240 14
    6 241 14
    6 242 14
    6 243 14
    6 244 14
    6 245 14
    6 246 14
    6 247 14
    6 248 14
    6 249 14
    6 250 15
    6 251 15
    6 252 15
    6 253 15
    6 254 15
    6 255 15
    6 256 15
    6 257 15
    6 258 15
    6 259 15
    6 260 15
    6 261 15
    6 262 15
    6 263 15
    6 264 15
    6 265 15
    6 266 15
    6 267 15
    6 268 15
    6 269 15
    6 270 15
    6 271 15
    6 272 15
    6 273 15
    6 274 15
    6 275 15
    6 276 15
    6 277 15
    6 278 15
    6 279 15
    6 280 15
    6 281 15
    6 282 15
    6 283 15
    6 284 15
    6 285 15
    6 286 15
    6 287 15
    6 288 15
       

Definition in file Datak6.hpp.