THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. March 2001), DS #5.

Venn Diagram Survey Hamburger's Symmetric Diagram for n = 11

Sector 1:
Sector 2:
Sector 3:
Sector 4:
Sector 5:
Sector 6:
Sector 7:
Sector 8:
Sector 9:
Sector 10:
Sector 11:

How to check the diagram

Sector 1:

Sector 1 with dual graph superimposed:
Dual graph of a sector:

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

 THE ELECTRONIC JOURNAL OF COMBINATORICS (ed. March 2001), DS #5.