$12^{2}_{150}$ - Minimal pinning sets
Pinning sets for 12^2_150 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_150 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 96
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: 2.91189
on average over minimal pinning sets: 2.16667
on average over optimal pinning sets: 2.16667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 4, 7, 9}
6
[2, 2, 2, 2, 2, 3]
2.17
B (optimal)
• {1, 2, 3, 4, 7, 10}
6
[2, 2, 2, 2, 2, 3]
2.17
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
6
2
0
0
2.17
7
0
0
11
2.52
8
0
0
25
2.78
9
0
0
30
2.98
10
0
0
20
3.13
11
0
0
7
3.25
12
0
0
1
3.33
Total
2
0
94
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 3, 4, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,7,7],[0,8,1,0],[1,8,6,5],[1,4,6,6],[2,5,5,4],[2,9,9,2],[3,9,9,4],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[6,20,1,7],[7,19,8,18],[5,15,6,16],[19,1,20,2],[8,12,9,11],[17,10,18,11],[16,10,17,9],[14,4,15,5],[2,13,3,12],[3,13,4,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(13,4,-14,-5)(17,10,-18,-11)(11,18,-12,-19)(19,16,-20,-17)(20,5,-7,-6)(6,7,-1,-8)(2,9,-3,-10)(12,15,-13,-16)(3,14,-4,-15)
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)(-2,-10,17,-20,-6,-8)(-3,-15,12,18,10)(-4,13,15)(-5,20,16,-13)(-7,6)(-9,2)(-11,-19,-17)(-12,-16,19)(-14,3,9,1,7,5)(-18,11)(4,14)
Multiloop annotated with half-edges
12^2_150 annotated with half-edges