$12^{2}_{147}$ - Minimal pinning sets
Pinning sets for 12^2_147 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_147 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 192
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.96906
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 5, 7}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 3, 5, 8}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.2
6
0
0
13
2.54
7
0
0
36
2.78
8
0
0
55
2.95
9
0
0
50
3.09
10
0
0
27
3.19
11
0
0
8
3.27
12
0
0
1
3.33
Total
2
0
190
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,6,7],[0,7,1,0],[1,7,8,5],[1,4,8,8],[2,9,9,2],[2,9,4,3],[4,9,5,5],[6,8,7,6]]
PD code (use to draw this multiloop with SnapPy): [[6,20,1,7],[7,19,8,18],[5,13,6,14],[19,1,20,2],[8,12,9,11],[17,10,18,11],[14,4,15,5],[12,2,13,3],[9,16,10,17],[3,15,4,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,6,-8,-1)(12,3,-13,-4)(19,4,-20,-5)(10,17,-11,-18)(18,15,-19,-16)(1,20,-2,-7)(5,8,-6,-9)(16,9,-17,-10)(11,14,-12,-15)(2,13,-3,-14)
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,-7)(-2,-14,11,17,9,-6,7)(-3,12,14)(-4,19,15,-12)(-5,-9,16,-19)(-8,5,-20,1)(-10,-18,-16)(-11,-15,18)(-13,2,20,4)(-17,10)(3,13)(6,8)
Multiloop annotated with half-edges
12^2_147 annotated with half-edges