$12^{2}_{130}$ - Minimal pinning sets
Pinning sets for 12^2_130 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_130 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 128
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: 2.90623
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, 2, 3, 6, 9}
5
[2, 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
5
1
0
0
2.0
6
0
0
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,6],[0,7,8,4],[1,3,5,1],[2,4,9,9],[2,9,7,2],[3,6,8,8],[3,7,7,9],[5,8,6,5]]
PD code (use to draw this multiloop with SnapPy): [[7,16,8,1],[15,6,16,7],[8,17,9,20],[1,4,2,5],[5,14,6,15],[17,14,18,13],[9,19,10,20],[10,3,11,4],[2,11,3,12],[18,12,19,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(15,2,-16,-3)(13,4,-14,-5)(16,9,-1,-10)(19,10,-20,-11)(11,18,-12,-19)(3,12,-4,-13)(5,14,-6,-15)(7,20,-8,-17)(17,6,-18,-7)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,20,10)(-2,15,-6,17,-8)(-3,-13,-5,-15)(-4,13)(-7,-17)(-9,16,2)(-10,19,-12,3,-16)(-11,-19)(-14,5)(-18,11,-20,7)(1,9)(4,12,18,6,14)
Multiloop annotated with half-edges
12^2_130 annotated with half-edges