$12^{2}_{226}$ - Minimal pinning sets
Pinning sets for 12^2_226 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_226 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)
• {1, 3, 5, 7}
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, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,6],[0,6,7,4],[1,3,8,8],[2,9,6,6],[2,5,5,3],[3,9,9,8],[4,7,9,4],[5,8,7,7]]
PD code (use to draw this multiloop with SnapPy): [[14,20,1,15],[15,13,16,14],[16,19,17,20],[1,6,2,7],[7,12,8,13],[4,18,5,19],[17,5,18,6],[2,10,3,9],[11,8,12,9],[3,10,4,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,1,-15,-2)(11,2,-12,-3)(7,4,-8,-5)(5,12,-6,-13)(13,6,-14,-7)(3,8,-4,-9)(18,9,-19,-10)(14,15,-1,-16)(19,16,-20,-17)(10,17,-11,-18)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,20,16)(-2,11,17,-20)(-3,-9,18,-11)(-4,7,-14,-16,19,9)(-5,-13,-7)(-6,13)(-8,3,-12,5)(-10,-18)(-15,14,6,12,2)(-17,10,-19)(1,15)(4,8)
Multiloop annotated with half-edges
12^2_226 annotated with half-edges