OKlibrary  0.2.1.6
Datak5.hpp File Reference

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 5 (length of arithmetic progressions) More...

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Detailed Description

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 5 (length of arithmetic progressions)

Todo:
Elementary statistics
  • Investigating tr_arithprog_hg(5,n).
  • The numbers of minimum hyperedges:
    L5 : [];
    minimum_transversals_decomp_gen(inf,lambda([n],arithprog_primes_hg(5,n)), 'L5)$
    
    1 1 0 [0,1,1]
    10 10 1 [1,5,6]
    16 16 2 [1,3,10]
    31 31 3 [2,15,21]
    32 32 4 [3,90,19]
    37 37 5 [3,72,23]
    40 40 6 [3,28,23]
    45 45 7 [3,20,26]
    49 49 8 [4,108,26]
    54 54 9 [4,68,29]
    55 55 10 [4,56,29]
    58 58 11 [5,280,28]
    61 61 12 [6,1400,27]
    62 62 13 [7,10100,25]
    64 64 14 [7,6600,26]
    71 71 15 [7,4200,32]
    74 74 16 [7,1680,32]
    77 77 17 [7,1680,34]
    78 78 18 [8,8400,31]
    82 82 19 [8,3360,32]
    86 86 20 [8,960,33]
    87 87 21 [9,4800,30]
    90 90 22 [9,4800,32]
    92 92 23 [9,1920,32]
    97 97 26 [9,80,35]
    98 98 27 [10,400,32]
    107 107 28 [11,12000,38]
    111 111 29 [11,2400,39]
    112 112 30 [12,14400,38]
    113 113 31 [12,480,37]
    121 121 32 [13,2400,41]
    122 122 33 [13,200,39]
    123 123 34 [14,15000,37]
    125 125 35 [14,12000,38]
    128 128 36 [14,2560,38]
    134 134 37 [14,2560,43]
    135 135 38 [14,1024,41]
    141 141 39 [14,512,45]
    142 142 40 [15,7104,44]
    143 143 42 [16,333888,43]
    146 146 43 [16,330880,45]
    147 147 44 [16,140800,44]
    149 149 45 [17,704000,42]
    150 150 47 [18,704000,37]
    152 152 49 [18,204800,37]
    154 154 50 [19,4211200,38]
    155 155 51 [19,4211200,38]
    
    T : transform_steps_l(map(lambda([d],d[4][1]),reverse(L5)));
     [9,30,31,48,57,60,61,77,86,97,106,111,120,122,141,142,148,149,153]
    length(T);
     19
       
  • So here we are definitely better than what minisat2 can compute (see below --- which of course uses a very simple problem representation).
Todo:
Only computing the transversal numbers
  • Just computing the transversal numbers, using minisat2 and the direct translation (as provided by "GTTransversalsInc 5 1 0 OutputFile"):
    k n tau
    5 1 0
    5 2 0
    5 3 0
    5 4 0
    5 5 0
    5 6 0
    5 7 0
    5 8 0
    5 9 0
    5 10 1
    5 11 1
    5 12 1
    5 13 1
    5 14 1
    5 15 1
    5 16 1
    5 17 1
    5 18 1
    5 19 1
    5 20 1
    5 21 1
    5 22 1
    5 23 1
    5 24 1
    5 25 1
    5 26 1
    5 27 1
    5 28 1
    5 29 1
    5 30 1
    5 31 2
    5 32 3
    5 33 3
    5 34 3
    5 35 3
    5 36 3
    5 37 3
    5 38 3
    5 39 3
    5 40 3
    5 41 3
    5 42 3
    5 43 3
    5 44 3
    5 45 3
    5 46 3
    5 47 3
    5 48 3
    5 49 4
    5 50 4
    5 51 4
    5 52 4
    5 53 4
    5 54 4
    5 55 4
    5 56 4
    5 57 4
    5 58 5
    5 59 5
    5 60 5
    5 61 6
    5 62 7
    5 63 7
    5 64 7
    5 65 7
    5 66 7
    5 67 7
    5 68 7
    5 69 7
    5 70 7
    5 71 7
    5 72 7
    5 73 7
    5 74 7
    5 75 7
    5 76 7
    5 77 7
    5 78 8
    5 79 8
    5 80 8
    5 81 8
    5 82 8
    5 83 8
    5 84 8
    5 85 8
    5 86 8
    5 87 9
    5 88 9
    5 89 9
    5 90 9
    5 91 9
    5 92 9
    5 93 9
    5 94 9
    5 95 9
    5 96 9
    5 97 9
    5 98 10
    5 99 10
    5 100 10
    5 101 10
    5 102 10
    5 103 10
    5 104 10
    5 105 10
    5 106 10
    5 107 11
    5 108 11
    5 109 11
    5 110 11
    5 111 11
    5 112 12
    5 113 12
    5 114 12
    5 115 12
    5 116 12
    5 117 12
    5 118 12
    5 119 12
    5 120 12
    5 121 13
    5 122 13
    5 123 14
    5 124 14
    5 125 14
    5 126 14
    5 127 14
    5 128 14
    5 129 14
    5 130 14
    5 131 14
    5 132 14
    5 133 14
    5 134 14
       

Definition in file Datak5.hpp.