$12^{2}_{160}$ - Minimal pinning sets
Pinning sets for 12^2_160 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_160 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 256
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.96564
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {2, 3, 7, 11}
4
[2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,7,8,8],[0,8,4,4],[0,3,3,5],[1,4,9,1],[1,9,7,7],[2,6,6,9],[2,9,3,2],[5,8,7,6]]
PD code (use to draw this multiloop with SnapPy): [[10,3,1,4],[4,11,5,20],[9,17,10,18],[2,7,3,8],[1,7,2,6],[11,6,12,5],[19,14,20,15],[18,14,19,13],[16,8,17,9],[12,16,13,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(3,12,-4,-13)(4,9,-5,-10)(10,5,-1,-6)(17,6,-18,-7)(14,19,-15,-20)(20,15,-11,-16)(16,13,-17,-14)(7,18,-8,-19)(11,2,-12,-3)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,18,6)(-2,11,15,19,-8)(-3,-13,16,-11)(-4,-10,-6,17,13)(-5,10)(-7,-19,14,-17)(-9,4,12,2)(-12,3)(-14,-20,-16)(-15,20)(-18,7)(1,5,9)
Multiloop annotated with half-edges
12^2_160 annotated with half-edges