OKlibrary  0.2.1.6
Datak7.hpp File Reference

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 7 (length of arithmetic progressions) More...

Go to the source code of this file.


Detailed Description

Investigating the transversal hypergraph of Green-Tao hypergraphs for k = 7 (length of arithmetic progressions)

Todo:
Elementary statistics
  • Investigating tr_arithprog_hg(7,n).
  • The numbers of minimum hyperedges:
    L7 : [];
    minimum_transversals_decomp_gen(inf,lambda([n],arithprog_primes_hg(7,n)),'L7)$
    
    1 1 0 [0,1,1]
    155 155 1 [1,7,149]
    214 214 2 [2,49,202]
    228 228 3 [3,343,210]
    232 232 4 [4,2401,208]
    263 263 5 [4,2058,238]
    289 289 6 [4,1715,263]
    316 316 7 [4,1372,289]
    323 323 8 [5,9604,290]
    349 349 9 [5,8232,315]
    396 396 11 [6,32928,353]
    570 570 12 [7,230496,521]
    641 641 14 [8,921984,583]
    665 665 15 [8,691488,606]
    690 690 17 [8,691488,630]
    715 715 18 [9,4840416,649]
    789 789 19 [9,4148928,722]
    796 796 20 [10,29042496,723]
    827 827 21 [11,203297472,748]
    872 872 22 [12,1423082304,787]
    875 875 23 [13,9961576128,784]
    1000 1000 24 [13,4269246912,905]
    1048 1048 25 [14,29884728384,947]
    1078 1078 26 [14,4269246912,971]
    1125 1125 27 [15,29884728384,1012]
    1158 1158 28 [16,209193098688,1039]
    1176 1176 29 [16,34865516448,1051]
    1180 1180 30 [17,244058615136,1049]
    1188 1188 31 [18,1708410305952,1051]
    1205 1205 32 [18,488117230272,1063]
    1240 1240 33 [18,69731032896,1092]
    1304 1304 34 [19,488117230272,1150]
    1323 1323 35 [19,418386197376,1168]
    1343 1343 36 [20,2928703381632,1182]
    1357 1357 37 [20,418386197376,1190]
    1373 1373 38 [21,2928703381632,1200]
    1376 1376 39 [21,836772394752,1198]
    1398 1398 40 [22,5857406763264,1214]
    1413 1413 41 [22,836772394752,1223]
    1424 1424 42 [23,5857406763264,1228]
    1428 1428 43 [23,5020634368512,1231]
    1447 1447 44 [23,4303400887296,1249]
    1452 1452 45 [24,30123806211072,1248]
    1453 1453 46 [24,25103171842560,1248]
    1454 1454 47 [24,3586167406080,1243]
    1473 1473 48 [24,3073857776640,1261]
    1497 1497 49 [24,2561548147200,1284]
    1508 1508 50 [25,46107866649600,1290]
    1523 1523 53 [25,7684644441600,1299]
    1542 1542 54 [26,53792511091200,1312]
    1555 1555 55 [26,53792511091200,1324]
    1556 1556 56 [27,376547577638400,1319]
    1564 1564 57 [28,2635833043468800,1321]
    1569 1569 58 [28,2635833043468800,1325]
    1572 1572 59 [29,19768747826016000,1322]
    1647 1647 60 [29,2824106832288000,1391]
    1656 1656 61 [29,1129642732915200,1396]
    1688 1688 62 [30,8095772919225600,1422]
    1694 1694 63 [31,58019705921116800,1422]
    1733 1733 64 [32,406137941447817600,1455]
    1743 1743 65 [32,58019705921116800,1460]
    1747 1747 66 [33,406137941447817600,1458]
    1748 1748 67 [33,157942532785262400,1454]
    1762 1762 68 [34,1342511528674730400,1463]
    1768 1768 69 [35,9397580700723112800,1463]
    1777 1777 70 [36,65783064905061789600,1466]
    1778 1778 71 [37,460481454335432527200,1461]
    1801 1801 72 [37,394698389430370737600,1483]
    1820 1820 73 [38,2762888726012595163200,1496]
    1825 1825 74 [39,19340221082088166142400,1495]
    1831 1831 75 [40,135381547574617162996800,1495]
    1853 1853 76 [41,947670833022320140977600,1511]
    1857 1857 77 [41,947670833022320140977600,1514]
    1869 1869 78 [41,135381547574617162996800,1520]
    1881 1881 79 [41,116041326492528996854400,1531]
    1892 1892 81 [41,16577332356075570979200,1533]
    1903 1903 82 [42,116041326492528996854400,1538]
    1914 1914 83 [42,23208265298505799370880,1543]
    1915 1915 84 [42,19969902698714292481920,1543]
    1918 1918 85 [42,5639341293656860003200,1540]
    1935 1935 86 [42,4833721108848737145600,1556]
    1954 1954 87 [43,33836047761941160019200,1569]
    1961 1961 89 [44,33836047761941160019200,1564]
    1979 1979 90 [45,4060325731432939202304000,1581]
    1980 1980 91 [46,28422280120030574416128000,1576]
    2009 2009 92 [46,4060325731432939202304000,1599]
    2022 2022 93 [46,3383604776194116001920000,1611]
    2028 2028 94 [47,24249167562724498013760000,1611]
    2032 2032 95 [47,3464166794674928287680000,1609]
    2117 2117 96 [47,3464166794674928287680000,1693]
    2145 2145 97 [47,494880970667846898240000,1715]
    2191 2191 98 [48,3464166794674928287680000,1755]
    2198 2198 99 [49,24249167562724498013760000,1756]
    2203 2203 100 [49,3464166794674928287680000,1755]
    2261 2261 101 [49,3464166794674928287680000,1812]
    2265 2265 102 [50,24249167562724498013760000,1810]
    2285 2285 103 [50,24249167562724498013760000,1829]
    2317 2317 104 [51,169744172939071486096320000,1855]
    2331 2331 105 [51,85870581604471457672256000,1864]
    2363 2363 106 [51,12267225943495922524608000,1890]
    2365 2365 107 [52,138444407076596839920576000,1888]
    2372 2372 108 [53,969110849536177879444032000,1889]
    2396 2396 109 [53,969110849536177879444032000,1910]
    2406 2406 110 [53,969110849536177879444032000,1919]
    2411 2411 111 [54,6783775946753245156108224000,1918]
    2415 2415 112 [54,969110849536177879444032000,1916]
    2420 2420 113 [54,138444407076596839920576000,1915]
    2436 2436 114 [54,23074067846099473320096000,1925]
    2437 2437 115 [54,19777772439513834274368000,1925]
    2468 2468 116 [55,138444407076596839920576000,1950]
    2490 2490 117 [55,25381474630709420652105600,1969]
    2499 2499 118 [55,25381474630709420652105600,1977]
    2503 2503 119 [56,761444238921282619563168000,1977]
    2504 2504 120 [57,11040941464358597983665936000,1974]
    2515 2515 121 [57,11040941464358597983665936000,1984]
    2561 2561 122 [58,77286590250510185885661552000,2024]
    2568 2568 123 [59,1159298853757652788284923280000,2030]
    2573 2573 124 [59,993684731792273818529934240000,2034]
    2647 2647 125 [59,141954961684610545504276320000,2102]
    2651 2651 127 [60,1703459540215326546051315840000,2100]
    2664 2664 129 [61,3367303742286110614287484800000,2101]
    2667 2667 130 [62,60611467361149991057174726400000,2100]
    2672 2672 131 [62,60611467361149991057174726400000,2104]
    2684 2684 132 [63,424280271528049937400223084800000,2110]
    2698 2698 133 [63,70713378588008322900037180800000,2118]
    2724 2724 134 [63,18760692278451187708173129600000,2138]
    2738 2738 135 [63,12791381098943991619208952000000,2151]
    2788 2788 136 [64,89539667692607941334462664000000,2195]
    2816 2816 137 [64,76748286593663949715253712000000,2222]
    2817 2817 138 [64,40631445843704443966899024000000,2219]
    2820 2820 139 [65,314893705288709440743467436000000,2216]
    2823 2823 140 [65,314893705288709440743467436000000,2218]
    2824 2824 141 [65,15943985077909338771821136000000,2214]
    2829 2829 142 [66,183355828395957395875943064000000,2214]
    2870 2870 143 [66,183355828395957395875943064000000,2254]
    2873 2873 144 [66,15279652366329782989661922000000,2252]
    2915 2915 145 [66,15279652366329782989661922000000,2293]
    2935 2935 146 [66,2182807480904254712808846000000,2307]
    2938 2938 147 [66,72760249363475157093628200000,2304]
    2943 2943 148 [66,12126708227245859515604700000,2304]
    2945 2945 149 [67,201303356572281267959038020000,2301]
    2955 2955 150 [67,28757622367468752565576860000,2305]
    2969 2969 151 [68,201303356572281267959038020000,2313]
    2986 2986 152 [69,1409123496005968875713266140000,2324]
    2989 2989 153 [70,9863864472041782129992862980000,2321]
    3026 3026 154 [71,69047051304292474909950040860000,2352]
    3029 3029 155 [72,759517564347217224009450449460000,2349]
    3039 3039 156 [73,5316622950430520568066153146220000,2353]
    3084 3084 157 [73,886103825071753428011025524370000,2392]
    3097 3097 158 [74,11519349725932794564143331816810000,2399]
    3129 3129 159 [75,437735289585446193437446609038780000,2430]
    3139 3139 160 [75,62533612797920884776778087005540000,2434]
    3140 3140 161 [76,2688945350310598045401457741238220000,2434]
    3167 3167 162 [77,18822617452174186317810204188667540000,2455]
    3170 3170 163 [78,131758322165219304224671429320672780000,2452]
    3174 3174 164 [79,922308255156535129572700005244709460000,2450]
    3179 3179 165 [80,6456157786095745907008900036712966220000,2449]
    3180 3180 166 [81,116210840149723426326160200660833391960000,2445]
    3208 3208 167 [82,813475881048063984283121404625833743720000,2467]
    3215 3215 168 [82,813475881048063984283121404625833743720000,2473]
    3241 3241 169 [83,147239134469699581155244974237275907613320000,2498]
    3247 3247 170 [83,126204972402599640990209977917665063668560000,2503]
    3251 3251 171 [83,7011387355699980055011665439870281314920000,2501]
    3252 3252 172 [83,609685857017389570001014386075676636080000,2496]
    3253 3253 173 [83,575814420516423482778735809071472378520000,2496]
    3275 3275 174 [84,4030700943614964379451150663500306649640000,2512]
    3284 3284 175 [84,806140188722992875890230132700061329928000,2515]
    3293 3293 176 [85,5642981321060950131231610928900429309496000,2518]
    3315 3315 177 [85,4724356454841725691263674266056173375392000,2539]
    3320 3320 178 [85,674908064977389384466239180865167625056000,2538]
    3324 3324 179 [85,634250952629353879377911519367265960896000,2541]
    3328 3328 180 [86,4439756668405477155645380635570861726272000,2539]
    3339 3339 181 [86,466051804970740695896476420308543496128000,2545]
    3380 3380 182 [87,3352983819095051117699649801664243486032000,2580]
    3397 3397 183 [87,2886932014124310421803173381355699989904000,2596]
    3405 3405 184 [87,412418859160615774543310483050814284272000,2598]
    3420 3420 185 [88,6403345444862192288961925921052116518960000,2607]
    3422 3422 186 [89,44823418114035346022733481447364815632720000,2603]
    3435 3435 187 [89,30844589414065000822423378758695110418448000,2613]
    3458 3458 188 [89,28565432560808966278894557668151136742208000,2635]
    3466 3466 189 [89,2197340966216074329145735205242395134016000,2637]
    3483 3483 190 [89,1883435113899492282124915890207767257728000,2653]
    3489 3489 191 [89,1614372954770993384678499334463800506624000,2658]
    3493 3493 192 [89,1383748246946565758295856572397543291392000,2661]
    3500 3500 193 [90,31134335556297729561656772878944724056320000,2663]
    3507 3507 194 [91,217940348894084106931597410152613068394240000,2664]
    3514 3514 195 [91,54485087223521026732899352538153267098560000,2667]
    3522 3522 196 [92,381395610564647187130295467767072869689920000,2669]
    3526 3526 199 [95,130818694423673985185691345444105994303642560000,2655]
    3544 3544 200 [95,112130309506006273016306867523519423688836480000,2672]
    3551 3551 201 [95,16018615643715181859472409646217060526976640000,2673]
    3552 3552 202 [95,10542165850992042762216884980843706500659840000,2670]
    3556 3556 203 [96,126505990211904513146602619770124478007918080000,2668]
    3561 3561 204 [96,11500544564718592104236601797284043455265280000,2668]
    3602 3602 205 [96,11500544564718592104236601797284043455265280000,2708]
    3603 3603 206 [97,80503811953030144729656212580988304186856960000,2703]
    3628 3628 207 [97,75768293602851900922029376546812521587630080000,2727]
    3633 3633 208 [98,530378055219963306454205635827687651113410560000,2726]
    3636 3636 209 [98,530378055219963306454205635827687651113410560000,2728]
    3643 3643 210 [99,3712646386539743145179439450793813557793873920000,2729]
    3649 3649 211 [99,604384295483214000378048282687364997780398080000,2729]
    3652 3652 212 [100,4230690068382498002646337978811554984462786560000,2726]
    3660 3660 213 [101,29614830478677486018524365851680884891239505920000,2728]
    3661 3661 214 [101,4230690068382498002646337978811554984462786560000,2723]
    3668 3668 215 [102,29614830478677486018524365851680884891239505920000,2724]
    3670 3670 216 [102,5670924985278667535462112609896339660024586240000,2722]
    3699 3699 217 [102,5670924985278667535462112609896339660024586240000,2750]
    3726 3726 218 [102,810132140754095362208873229985191380003512320000,2771]
    3737 3737 219 [102,277759591115689838471613678852065616001204224000,2776]
    3754 3754 220 [103,6943989777892245961790341971301640400030105600000,2788]
    3765 3765 221 [103,154310883953161021373118710473369786667335680000,2793]
    3766 3766 222 [103,57135516798983818409288851982851203809771520000,2788]
    3768 3768 223 [104,399948617592886728865021963879958426668400640000,2784]
    3772 3772 224 [104,342813100793902910455733111897107222858629120000,2787]
    3773 3773 226 [104,48973300113414701493676158842443888979804160000,2784]
    3775 3775 228 [104,27575056370165935525718557906781469020160000000,2783]
    3791 3791 229 [104,27575056370165935525718557906781469020160000000,2798]
    3802 3802 230 [105,330900676441991226308622694881377628241920000000,2803]
    3812 3812 231 [106,2346386614770483241097506381886132272988160000000,2807]
    3821 3821 232 [106,378788870545907608428296994385205209989120000000,2810]
    3881 3881 233 [107,27651587549851255415265680590119980329205760000000,2865]
    3882 3882 234 [107,4608597924975209235877613431686663388200960000000,2861]
    3887 3887 235 [108,32260185474826464651143294021806643717406720000000,2860]
    
    T : transform_steps_l(map(lambda([d],d[4][1]),reverse(L7)));
     [154,213,227,231,322,395,569,640,714,795,826,871,874,1047,1124,1157,1179,1187,1303,1342,1372,
           1397,1423,1451,1507,1541,1555,1563,1571,1687,1693,1732,1746,1761,1767,1776,1777,1819,1824,
           1830,1852,1902,1953,1960,1978,1979,2027,2190,2197,2264,2316,2364,2371,2410,2467,2502,2503,
           2560,2567,2650,2663,2666,2683,2787,2819,2828,2944,2968,2985,2988,3025,3028,3038,3096,3128,
           3139,3166,3169,3173,3178,3179,3207,3240,3274,3292,3327,3379,3419,3421,3499,3506,3521,3522,
           3524,3525,3555,3602,3632,3642,3651,3659,3667,3753,3767,3801,3811,3880,3886]
    length(T);
     108
       
Todo:
Only computing the transversal numbers
  • Just computing the transversal numbers, using minisat2 and the direct translation:
    > GTTransversalsInc 7 1 0 GT_7 GT_7_SAT
    
    transform_steps_l(map(third,rest(read_nested_list("GT_7"))));
      [154,213,227,231,322,395,569,640,714,795,826,871,874,1047,1124,1157,1179]
       
    Value 17 is attained for 1180 <= n <= 1187.
  • The computation for n=1180 seems hard --- one should be able to do much better!

Definition in file Datak7.hpp.