$12^{2}_{38}$ - Minimal pinning sets
Pinning sets for 12^2_38 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_38 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, 2, 3, 4, 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, 4, 4, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,4,0],[0,5,3,0],[1,2,6,7],[1,7,8,8],[2,8,8,6],[3,5,9,9],[3,9,9,4],[4,5,5,4],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,9,12,10],[19,1,20,2],[8,18,9,19],[12,5,13,4],[2,14,3,15],[15,7,16,8],[17,5,18,6],[13,3,14,4],[6,16,7,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,10,-12,-1)(1,20,-2,-11)(15,2,-16,-3)(13,4,-14,-5)(19,6,-20,-7)(17,8,-18,-9)(9,12,-10,-13)(3,14,-4,-15)(5,16,-6,-17)(7,18,-8,-19)
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,-11)(-2,15,-4,13,-10,11)(-3,-15)(-5,-17,-9,-13)(-6,19,-8,17)(-7,-19)(-12,9,-18,7,-20,1)(-14,3,-16,5)(2,20,6,16)(4,14)(8,18)(10,12)
Multiloop annotated with half-edges
12^2_38 annotated with half-edges