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| THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. June 2005), DS #5. |
Sector 1:
The necklaces in the following table are assigned to the vertices of the lattice left-to-right at a given level. The density of the necklace increases in the lattice from top-to-bottom. For example, there is an edge in the lattice from face #2 to face #7, corresponding to necklaces 11000000000 and 11100000000. Face #2 is the unique dual vertex at level 2, and face #7 is the leftmost dual vertex at level 3. Since these necklaces differ at bit position 3, the edge between them represents curve 3. To check that the diagram is correct one needs to (a) verify that adjacent vertices correspond to adjacent necklaces, and (b) that all the necklaces are rotationally distinct.
| # | Density 1 necklace | # | Density 10 necklace |
|---|---|---|---|
| 1 | 100 000 000 00 | 186 | 111 111 111 10 |
| # | Density 2 necklace | # | Density 9 necklace |
| 2 | 110 000 000 00 | 181 | 111 111 111 00 |
| 3 | 100 010 000 00 | 182 | 111 011 111 10 |
| 4 | 100 000 000 10 | 183 | 110 111 111 10 |
| 5 | 100 001 000 00 | 184 | 111 101 111 10 |
| 6 | 100 100 000 00 | 185 | 101 111 111 10 |
| # | Density 3 necklace | # | Density 8 necklace |
| 7 | 111 000 000 00 | 166 | 111 111 110 00 |
| 8 | 110 010 000 00 | 167 | 111 111 011 00 |
| 9 | 110 000 010 00 | 168 | 111 110 111 00 |
| 10 | 110 000 100 00 | 169 | 110 111 111 00 |
| 11 | 100 010 100 00 | 170 | 111 011 110 10 |
| 12 | 100 010 000 10 | 171 | 101 011 111 10 |
| 13 | 101 010 000 00 | 172 | 111 011 111 00 |
| 14 | 110 000 000 10 | 173 | 111 011 101 10 |
| 15 | 100 100 000 10 | 174 | 110 101 111 10 |
| 16 | 110 001 000 00 | 175 | 110 110 111 10 |
| 17 | 110 100 000 00 | 176 | 111 101 111 00 |
| 18 | 100 100 010 00 | 177 | 101 111 111 00 |
| 19 | 100 110 000 00 | 178 | 101 111 011 10 |
| 20 | 100 101 000 00 | 179 | 101 101 111 10 |
| 21 | 100 100 100 00 | 180 | 100 111 111 10 |
| # | Density 4 necklace | # | Density 7 necklace |
| 22 | 111 001 000 00 | 136 | 111 011 110 00 |
| 23 | 111 100 000 00 | 137 | 111 111 100 00 |
| 24 | 111 000 010 00 | 138 | 111 111 010 00 |
| 25 | 111 010 000 00 | 139 | 111 101 110 00 |
| 26 | 110 011 000 00 | 140 | 111 101 011 00 |
| 27 | 110 010 010 00 | 141 | 111 011 011 00 |
| 28 | 110 010 001 00 | 142 | 111 110 011 00 |
| 29 | 110 100 010 00 | 143 | 111 110 101 00 |
| 30 | 110 001 100 00 | 144 | 110 111 110 00 |
| 31 | 110 100 100 00 | 145 | 110 110 111 00 |
| 32 | 111 000 100 00 | 146 | 111 010 110 10 |
| 33 | 110 010 100 00 | 147 | 111 011 100 10 |
| 34 | 110 010 000 10 | 148 | 101 011 101 10 |
| 35 | 101 010 000 10 | 149 | 101 011 111 00 |
| 36 | 100 011 000 10 | 150 | 111 010 101 10 |
| 37 | 101 011 000 00 | 151 | 111 011 001 10 |
| 38 | 101 010 010 00 | 152 | 110 001 111 10 |
| 39 | 110 000 001 10 | 153 | 110 110 110 10 |
| 40 | 110 000 100 10 | 154 | 110 101 111 00 |
| 41 | 110 100 000 10 | 155 | 111 101 101 00 |
| 42 | 110 101 000 00 | 156 | 111 100 111 00 |
| 43 | 110 100 001 00 | 157 | 101 101 111 00 |
| 44 | 101 100 010 00 | 158 | 101 111 011 00 |
| 45 | 100 101 010 00 | 159 | 100 111 111 00 |
| 46 | 100 100 110 00 | 160 | 101 111 110 00 |
| 47 | 101 110 000 00 | 161 | 101 110 011 10 |
| 48 | 100 111 000 00 | 162 | 100 111 011 10 |
| 49 | 100 110 000 10 | 163 | 101 111 010 10 |
| 50 | 100 101 000 10 | 164 | 100 101 111 10 |
| 51 | 100 100 101 00 | 165 | 100 110 111 10 |
| # | Density 5 necklace | # | Density 6 necklace |
| 52 | 111 001 100 00 | 94 | 111 011 100 00 |
| 53 | 111 101 000 00 | 95 | 111 101 100 00 |
| 54 | 111 100 100 00 | 96 | 111 110 100 00 |
| 55 | 111 110 000 00 | 97 | 111 111 000 00 |
| 56 | 111 000 110 00 | 98 | 111 001 110 00 |
| 57 | 111 100 010 00 | 99 | 111 100 011 00 |
| 58 | 111 001 010 00 | 100 | 111 101 010 00 |
| 59 | 111 011 000 00 | 101 | 111 011 001 00 |
| 60 | 110 011 010 00 | 102 | 111 011 010 00 |
| 61 | 110 010 011 00 | 103 | 111 010 011 00 |
| 62 | 111 010 010 00 | 104 | 111 110 010 00 |
| 63 | 110 110 010 00 | 105 | 110 110 011 00 |
| 64 | 110 110 001 00 | 106 | 110 110 101 00 |
| 65 | 110 100 110 00 | 107 | 110 101 110 00 |
| 66 | 110 011 100 00 | 108 | 110 111 100 00 |
| 67 | 110 110 100 00 | 109 | 110 110 110 00 |
| 68 | 111 010 100 00 | 110 | 111 010 100 10 |
| 69 | 110 010 100 10 | 111 | 110 011 100 10 |
| 70 | 111 010 000 10 | 112 | 111 011 000 10 |
| 71 | 101 010 001 10 | 113 | 101 010 101 10 |
| 72 | 101 011 000 10 | 114 | 101 011 001 10 |
| 73 | 101 011 001 00 | 115 | 101 011 101 00 |
| 74 | 101 010 011 00 | 116 | 101 010 111 00 |
| 75 | 110 000 101 10 | 117 | 111 000 101 10 |
| 76 | 111 000 001 10 | 118 | 111 010 001 10 |
| 77 | 110 001 100 10 | 119 | 110 001 110 10 |
| 78 | 110 100 010 10 | 120 | 110 110 010 10 |
| 79 | 110 101 100 00 | 121 | 110 101 101 00 |
| 80 | 111 100 001 00 | 122 | 111 100 101 00 |
| 81 | 101 100 110 00 | 123 | 111 100 110 00 |
| 82 | 101 101 010 00 | 124 | 101 101 011 00 |
| 83 | 100 111 010 00 | 125 | 101 111 010 00 |
| 84 | 100 101 110 00 | 126 | 100 111 110 00 |
| 85 | 100 100 111 00 | 127 | 100 101 111 00 |
| 86 | 101 111 000 00 | 128 | 101 111 100 00 |
| 87 | 101 110 010 00 | 129 | 101 110 011 00 |
| 88 | 100 111 000 10 | 130 | 100 111 001 10 |
| 89 | 101 110 000 10 | 131 | 101 111 000 10 |
| 90 | 100 101 010 10 | 132 | 100 111 010 10 |
| 91 | 100 101 001 10 | 133 | 100 101 101 10 |
| 92 | 100 100 101 10 | 134 | 100 100 111 10 |
| 93 | 100 110 101 00 | 135 | 100 110 111 00 |
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| THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. June 2005), DS #5. |
