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Some numerical results |
The number of D12-mosaics of block-type ∏ i=112 xiλi and stabilizer type Ũ i for 1≤ i≤ 16 are:
Ũ 1: 320 x13 x2 x7+678 x15 x2 x5+760 x13 x3 x6+1140 x15 x3 x4+546 x14 x2 x6+195 x43+546 x2 x4 x6+2860 x1 x3 x42+ 1140 x3 x4 x5+1648 x12 x22 x6+1140 x14 x3 x5+11480 x13 x23 x3+28 x5 x7+14 x4 x8+7 x3 x9+349 x32 x6+309 x2 x52+44 x22 x8+2004 x22 x42+516 x23 x6+5554 x23 x32+2022 x24 x4+309 x12 x52+2412 x12 x25+7 x13 x9+2527 x13 x33+14 x14 x8+ 660 x14 x42+2022 x14 x24+28 x15 x7+29 x16 x6+349 x16 x32 +516 x16 x23+28 x17 x5+14 x18 x4+44 x18 x22+7 x19 x3+320 x17 x2 x3+3450 x1 x2 x4 x5+2300 x1 x2 x3 x6+17280 x1 x22 x3 x4+6900 x12 x2 x3 x5+11520 x13 x2 x3 x4+581 x34+8 x62+337 x26+320 x2 x3 x7 +5662 x2 x32 x4+3420 x22 x3 x5+226 x1 x5 x6+160 x1 x4 x7+80 x1 x3 x8+2290 x1 x32 x5+25 x1 x2 x9+7660 x1 x2 x33+480 x1 x22 x7+3430 x1 x23 x5+8600 x1 x24 x3+546 x12 x4 x6+320 x12 x3 x7+5662 x12 x32 x4+108 x12 x2 x8+4196 x12 x2 x42+17026 x12 x22 x32+8468 x12 x23 x4+1140 x13 x4 x5+3420 x13 x22 x5+5662 x14 x2 x32+4208 x14 x22 x4+3420 x15 x22 x3+546 x16 x2 x4,
Ũ 2: 4 x14 x2 x6+6 x43+4 x2 x4 x6+12 x12 x22 x6+5 x32 x6 +6 x2 x52+23 x22 x42+9 x23 x6+41 x23 x32+18 x24 x4+6 x12 x52+34 x12 x25+7 x14 x42+18 x14 x24+ x16 x6+5 x16 x32+9 x16 x23+8 x34+ x62+11 x26+18 x2 x32 x4+4 x1 2 x4 x6+18 x12 x32 x4+2 x12 x2 x8+24 x12 x2 x42+54 x12 x22 x32+32 x12 x23 x4+18 x14 x2 x32+14 x14 x22 x4+4 x16 x2 x4,
Ũ 3: 20 x13 x2 x7+30 x15 x2 x5+19 x13 x3 x6+30 x15 x3 x4+28 x14 x2 x6+23 x43+28 x2 x4 x6+55 x1 x3 x42+30 x3 x4 x5+64 x1 2 x22 x6+30 x14 x3 x5+137 x13 x23 x3+10 x5 x7+6 x4 x8+4 x3 x9+26 x32 x6+2 x2 x10+19 x2 x52+14 x22 x8+66 x22 x42+43 x23 x6+117 x23 x3 2+88 x24 x4+ x1 x11+2 x12 x10+19 x12 x52+90 x12 x25+4 x13 x9+76 x13 x33+6 x14 x8+38 x14 x42+88 x14 x24+10 x15 x7+8 x16 x6+26 x16 x32+43 x16 x23+10 x17 x5+6 x18 x4+14 x18 x22+4 x19 x3+20 x17 x2 x3+30 x1 x2 x4 x5+20 x1 x2 x3 x6+90 x1 x22 x3 x4+60 x12 x2 x3 x5+60 x13 x2 x3 x4+2 x110 x2+33 x34+4 x62+33 x26+20 x2 x3 x7+86 x2 x32 x4+90 x22 x3 x5+10 x1 x5 x6+10 x1 x4 x7+5 x1 x3 x8+40 x1 x32 x5+5 x1 x2 x9+80 x1 x2 x33+30 x1 x22 x7+70 x1 x23 x5+125 x1 x24 x3+28 x12 x4 x6+20 x12 x3 x7+86 x12 x32 x4+14 x12 x2 x8+78 x12 x2 x42+178 x12 x22 x32+144 x1 2 x23 x4+30 x13 x4 x5+90 x13 x22 x5+86 x14 x2 x32+98 x14 x22 x4+90 x15 x22 x3 +28 x16 x2 x4,
Ũ 4: 30 x14 x2 x6 +55 x43+30 x2 x4 x6+90 x12 x22 x6+6 x4 x8+39 x32 x6+3 x2 x10+48 x2 x52+18 x22 x8 +216 x22 x42+67 x23 x6+277 x2 3 x32+168 x24 x4+3 x12 x10+48 x12 x52+243 x12 x25+6 x14 x8+72 x14 x42+168 x14 x24+ 9 x16 x6+39 x16 x32+67 x16 x23+6 x18 x4+18 x18 x22+3 x110 x2+72 x34+15 x62+130 x26+120 x2 x32 x4+30 x12 x4 x6+120 x12 x32 x4+15 x12 x2 x8+165 x12 x2 x42+360 x12 x22 x32+210 x12 x23 x4+120 x1 4 x2 x32+126 x14 x22 x4+30 x16 x2 x4,
Ũ 5: x13 x3 x6+ x4 3+3 x13 x23 x3+3 x13 x33+3 x34,
Ũ 6: x34+ x14 x22 x4,
Ũ 7: 2 x14 x2 x6+2 x43+2 x2 x4 x6+6 x12 x22 x6+ x4 x8+3 x3 2 x6+ x2 x10+4 x2 x52+3 x2 2 x8+5 x22 x42+5 x23 x6+11 x23 x32+7 x24 x4+ x12 x10+ 4 x12 x52+13 x12 x25+ x14 x8+3 x14 x42+7 x14 x24+ x16 x6+3 x16 x32+5 x16 x23 + x18 x4+3 x18 x22+ x110 x2+2 x34+4 x26+4 x2 x32 x4+ 2 x12 x4 x6+4 x12 x32 x4+ x12 x2 x8+7 x12 x2 x42+ 12 x12 x22 x32+6 x12 x23 x4+4 x14 x2 x32+7 x14 x22 x4+2 x16 x2 x4,
Ũ 8: 7 x43+ x4 x8+4 x22 x8+30 x22 x42+17 x24 x4+ x14 x8+9 x14 x42+ 17 x14 x24+ x18 x4+4 x18 x22+6 x34+4 x62+26 x26+9 x14 x22 x4,
Ũ 10: x13 x3 x6+ x43+3 x13 x23 x3+ x3 x9+ x23 x6+ x23 x32+ x13 x9+4 x13 x33+ x16 x23+ x19 x3+3 x34+ x26,
Ũ 11: 3 x16 x23+ x16 x32+ x16 x6+4 x26+3 x23 x32+3 x23 x6+ x32 x6+3 x43,
Ũ 12: 5 x1 4 x24+3 x14 x42+ x14 x8+ x18 x22+4 x26+3 x22 x42+ x22 x8+ x18 x4+5 x24 x4+2 x43+ x4 x8+3 x34+ x62,
Ũ 13: x16 x23+ x16 x32+ x16 x6+ x23 x32+ x23 x6+ x32 x6,
Ũ 14: 3 x26 + x43+ x62,
Ũ 16: x12+ x62+ x43+ x34+ x26+ x112 Acknowledgements
The author wants to thank Prof. R. Morris and B. Alegant for very useful and helpful discussions while preparing this article.
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Some numerical results |  |