OKlibrary  0.2.1.6
Datak9.hpp File Reference

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 9 (length of arithmetic progressions) More...

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Detailed Description

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 9 (length of arithmetic progressions)

Todo:
Elementary statistics
  • Investigating tr_arithprog_hg(9,n).
  • The numbers of minimum hyperedges:
    L9 : [];
    minimum_transversals_decomp_gen(inf,lambda([n],arithprog_primes_hg(9,n)),'L9)$
    
    T : transform_steps_l(map(lambda([d],d[4][1]),reverse(L9)));
     [288,689,1452,1496,1522,2021,2498,2822,2914,3314,3601,3774,4136,4550,4652,4710,4773,5121,
           5629,5704,6026,6282,6411,6492,6530,6764,6829,6848,6860,7380,7728,8330,8377,8504,8519,8530,
           8572,8700,8877,9043,9153,9180,9341,9396,9457,9526,9681,9755,10129,10424,10492,10664,10683,
           11268,11506,11605,11695,11948,12311,12475,12959,12980,13336,13414,13541,13667,13895,14068,
           14205,14270,14279,14736,14836,15088,15431,15433,15789,15861,15900,15966,16250,16380,16499,
           16962,17036,17050,17053,17208,17404,17600,17612,17620,17650,17936,18073,18219,18384,18463,
           18481,18559,18580,18596,18680,18736,18853,18959,19452,19560,19717,20020,20244,20283,20358,
           20382,20406,20440,20441,20473,20732,20991,21003,21144,21456,21627,21659,21732,21747,21753,
           21851,21913,21965,22198,22387,22761,22771,22796,22819,22882,23133,23214,23597,23801,23809,
           23815,24109,24128,24709,24836,24853,25116,25338,25722,25771,25846,26015,26183,26327,26605,
           26691,27237,27276,27485,27631,28081,28159,28247,28410,28830,28957,29109,29385,29398,29601,
           29674,29880,30121,30182,30226,30415,30938,30962,31023,31024,31080,31110,31161,31299,31760,
           31817,31952,31969,32051,32235,32412,32475,32623,32930,33098,33118,33258,33418,33496,33499,
           33659,33777,33857,34019,34259,34295,34329,34585,34997,35020,35319,35466,35487,35527,35656,
           35774,36000,36014,36279,36284,36323,36400,36877,37066,37361,37666,37702,37759,37885,38132,
           38450,38595,38633,38873,38994,39088,39249,39521,39525,39560,39620,39676,39681,39683,39699,
           39883,39926,40012,40109,40334,40378,40618,40635,40691,41024,41047,41215,41318,41330,41514,
           41527,41636,41664,41811,41812,41814,42030,42102,42200,42324,42409,42639,42766,42776,42872,
           42911,42957,43059,43360,43368,43488,43584,43821,43951,44121,44122,44148,44155,44167,44192,
           44248,44300,44358,44423,44443,44450,44523,44620,44698,44718,44740,44918,44927,44979,45100,
           45143,45272,45333,45412,45784,45874,46059,46100,46160,46271,46305,46482,46505]
       
Todo:
Only computing the transversal numbers
  • Just computing the transversal numbers, using minisat2 and the direct translation:
    > GTTransversalsInc 9 1 0 GT_9 GT_9_SAT
    
    L : transform_steps_l(map(third,rest(read_nested_list("GT_9"))));
     [288,689,1452,1496,1522,2021,2498,2822,2914,3314,3601,3774,4136,4550]
    length(L);
     14
    
    > tail -1 GT_9
    9 4652 14
    
    > tail -40 GT_9_SAT
    |         0 |    8671    38516   128230 |    12838        0    nan |  0.000 % |
    |       101 |    8671    38516   128230 |    14122      101      9 |  8.805 % |
    
    ...
    |  17044357 |    8671    38516   128230 |   185146    83508     84 |  8.805 % |
    *** INTERRUPTED ***
    restarts              : 29
    conflicts             : 24608505       (429 /sec)
    decisions             : 46478865       (1.40 % random) (810 /sec)
    propagations          : 4415348685     (76943 /sec)
    conflict literals     : 2107067304     (60.14 % deleted)
    Memory used           : 171.43 MB
    CPU time              : 57384.7 s
       

Definition in file Datak9.hpp.