$12^{2}_{161}$ - Minimal pinning sets
Pinning sets for 12^2_161 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_161 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, 5, 9}
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, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,6,7,7],[0,7,4,4],[0,3,3,5],[1,4,8,1],[1,8,9,2],[2,9,3,2],[5,9,9,6],[6,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[10,3,1,4],[4,11,5,20],[9,15,10,16],[2,7,3,8],[1,7,2,6],[11,6,12,5],[19,16,20,17],[14,8,15,9],[12,18,13,17],[13,18,14,19]]
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)(15,6,-16,-7)(7,16,-8,-17)(20,17,-11,-18)(18,13,-19,-14)(14,19,-15,-20)(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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,16,6)(-2,11,17,-8)(-3,-13,18,-11)(-4,-10,-6,15,19,13)(-5,10)(-7,-17,20,-15)(-9,4,12,2)(-12,3)(-14,-20,-18)(-16,7)(-19,14)(1,5,9)
Multiloop annotated with half-edges
12^2_161 annotated with half-edges