- Minimal pinning sets
Pinning sets for 12^2_86 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_86 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 192
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: 2.96906
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {2, 4, 6, 7, 11}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {2, 4, 5, 7, 11}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.2
6
0
0
13
2.54
7
0
0
36
2.78
8
0
0
55
2.95
9
0
0
50
3.09
10
0
0
27
3.19
11
0
0
8
3.27
12
0
0
1
3.33
Total
2
0
190
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,7,7],[0,7,8,9],[0,5,1,1],[1,4,6,6],[2,5,5,9],[2,8,3,2],[3,7,9,9],[3,8,8,6]]
PD code (use to draw this multiloop with SnapPy): [[3,10,4,1],[2,20,3,11],[9,17,10,18],[4,8,5,7],[1,12,2,11],[12,19,13,20],[18,13,19,14],[16,8,17,9],[5,16,6,15],[6,14,7,15]]
Permutation representation (action on half-edges):
Vertex permutation (5,2,-6,-3)(17,6,-18,-7)(1,8,-2,-9)(19,14,-20,-15)(4,15,-5,-16)(16,3,-17,-4)(7,18,-8,-19)(13,20,-14,-11)(10,11,-1,-12)(12,9,-13,-10)
Edge permutation (-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 (-1,-9,12)(-2,5,15,-20,13,9)(-3,16,-5)(-4,-16)(-6,17,3)(-7,-19,-15,4,-17)(-8,1,11,-14,19)(-10,-12)(-11,10,-13)(-18,7)(2,8,18,6)(14,20)
Multiloop annotated with half-edges
12^2_86 annotated with half-edges