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$8^{3}_{2}$ - Minimal pinning sets

Pinning sets for 8^3_2

Minimal pinning semi-lattice

(y-axis: cardinality)

Pinning semi lattice for 8^3_2

Pinning data

Refined data for the minimal pinning sets

Pin label Pin color Regions Cardinality Degree sequence Mean-degree
A (optimal) {1, 4, 5, 8} 4 [3, 3, 3, 3] 3.00
B (optimal) {2, 3, 6, 7} 4 [3, 3, 3, 3] 3.00
a (minimal) {1, 2, 3, 5, 6, 8} 6 [3, 3, 3, 3, 3, 3] 3.00
b (minimal) {1, 2, 4, 5, 6, 7} 6 [3, 3, 3, 3, 3, 3] 3.00
c (minimal) {2, 3, 4, 5, 7, 8} 6 [3, 3, 3, 3, 3, 3] 3.00
d (minimal) {1, 3, 4, 6, 7, 8} 6 [3, 3, 3, 3, 3, 3] 3.00

Data for pinning sets in each cardinal

Cardinality Optimal pinning sets Minimal suboptimal pinning sets Nonminimal pinning sets Averaged mean-degree
4 2 0 0 3.0
5 0 0 8 3.0
6 0 4 12 3.0
7 0 0 8 3.0
8 0 0 1 3.0
Total 2 4 29


Other information about this multiloop

Properties

Combinatorial encoding data

Multiloop annotated with half-edges

8^3_2 annotated with half-edges
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