$12^{2}_{208}$ - Minimal pinning sets
Pinning sets for 12^2_208 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_208 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 256
of which optimal: 3
of which minimal: 3
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.0346
on average over minimal pinning sets: 2.4
on average over optimal pinning sets: 2.4
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 4, 7, 11}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {1, 3, 5, 7, 11}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
• {1, 2, 4, 7, 11}
5
[2, 2, 2, 3, 3]
2.40
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
3
0
0
2.4
6
0
0
19
2.68
7
0
0
51
2.89
8
0
0
75
3.03
9
0
0
65
3.15
10
0
0
33
3.23
11
0
0
9
3.29
12
0
0
1
3.33
Total
3
0
253
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,5,5,3],[0,2,6,4],[1,3,6,7],[1,8,2,2],[3,9,7,4],[4,6,9,8],[5,7,9,9],[6,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[16,20,1,17],[17,15,18,16],[19,9,20,10],[1,9,2,8],[14,7,15,8],[18,11,19,10],[2,13,3,14],[3,6,4,7],[11,4,12,5],[5,12,6,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(1,4,-2,-5)(12,5,-13,-6)(6,15,-7,-16)(18,7,-19,-8)(8,17,-9,-18)(3,10,-4,-11)(16,11,-1,-12)(20,13,-17,-14)(14,19,-15,-20)
Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)(-11,11)(-12,12)(-13,13)(-14,14)(-15,15)(-16,16)(-17,17)(-18,18)(-19,19)(-20,20)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-5,12)(-2,9,17,13,5)(-3,-11,16,-7,18,-9)(-4,1,11)(-6,-16,-12)(-8,-18)(-10,3)(-13,20,-15,6)(-14,-20)(-17,8,-19,14)(2,4,10)(7,15,19)
Multiloop annotated with half-edges
12^2_208 annotated with half-edges