$12^{1}_{158}$ - Minimal pinning sets
Pinning sets for 12^1_158 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_158 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 128
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: 2.90623
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, 5, 11}
5
[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
5
1
0
0
2.0
6
0
0
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,5],[0,5,6,7],[1,7,7,8],[2,8,3,2],[3,9,9,7],[3,6,4,4],[4,9,9,5],[6,8,8,6]]
PD code (use to draw this loop with SnapPy): [[13,20,14,1],[19,12,20,13],[14,12,15,11],[1,16,2,17],[18,5,19,6],[15,10,16,11],[2,8,3,7],[17,7,18,6],[9,4,10,5],[8,4,9,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,5,-1,-6)(6,1,-7,-2)(15,2,-16,-3)(3,14,-4,-15)(4,19,-5,-20)(12,7,-13,-8)(8,11,-9,-12)(16,9,-17,-10)(18,13,-19,-14)(10,17,-11,-18)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,15,-4,-20,-6)(-3,-15)(-5,20)(-7,12,-9,16,2)(-8,-12)(-10,-18,-14,3,-16)(-11,8,-13,18)(-17,10)(-19,4,14)(1,5,19,13,7)(9,11,17)
Loop annotated with half-edges
12^1_158 annotated with half-edges