$12^{2}_{104}$ - Minimal pinning sets
Pinning sets for 12^2_104 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_104 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 256
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: 2.96564
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, 6, 7}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,5],[0,6,7,3],[0,2,8,8],[0,6,9,1],[1,9,9,1],[2,9,4,7],[2,6,8,8],[3,7,7,3],[4,6,5,5]]
PD code (use to draw this multiloop with SnapPy): [[5,10,6,1],[4,20,5,11],[13,9,14,10],[6,14,7,15],[1,12,2,11],[19,3,20,4],[12,17,13,18],[8,16,9,17],[7,16,8,15],[2,18,3,19]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,10,-12,-1)(15,6,-16,-7)(2,7,-3,-8)(3,16,-4,-17)(17,4,-18,-5)(5,18,-6,-19)(14,19,-15,-20)(9,20,-10,-11)(1,12,-2,-13)(13,8,-14,-9)
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,-13,-9,-11)(-2,-8,13)(-3,-17,-5,-19,14,8)(-4,17)(-6,15,19)(-7,2,12,10,20,-15)(-10,11)(-12,1)(-14,-20,9)(-16,3,7)(-18,5)(4,16,6,18)
Multiloop annotated with half-edges
12^2_104 annotated with half-edges