$12^{2}_{114}$ - Minimal pinning sets
Pinning sets for 12^2_114 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_114 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 64
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: 2.85421
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, 6, 7, 8, 9}
6
[2, 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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 8, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,4],[0,5,6,3],[0,2,1,0],[1,7,7,1],[2,8,6,6],[2,5,5,8],[4,9,9,4],[5,9,9,6],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[6,20,1,7],[7,19,8,18],[5,2,6,3],[19,1,20,2],[8,17,9,18],[3,14,4,13],[4,12,5,13],[16,9,17,10],[14,11,15,12],[10,15,11,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,4,-14,-5)(2,5,-3,-6)(10,17,-11,-18)(8,19,-9,-20)(1,20,-2,-7)(7,6,-8,-1)(18,9,-19,-10)(16,11,-17,-12)(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,-7)(-2,-6,7)(-3,-15,12,-17,10,-19,8,6)(-4,13,15)(-5,2,20,-9,18,-11,16,-13)(-8,-20,1)(-10,-18)(-12,-16)(-14,3,5)(4,14)(9,19)(11,17)
Multiloop annotated with half-edges
12^2_114 annotated with half-edges