$12^{1}_{147}$ - Minimal pinning sets
Pinning sets for 12^1_147
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_147
Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 96
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: 2.91189
on average over minimal pinning sets: 2.16667
on average over optimal pinning sets: 2.16667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
•
{1, 2, 3, 5, 7, 11}
6
[2, 2, 2, 2, 2, 3]
2.17
B (optimal)
•
{1, 2, 4, 5, 7, 11}
6
[2, 2, 2, 2, 2, 3]
2.17
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
6
2
0
0
2.17
7
0
0
11
2.52
8
0
0
25
2.78
9
0
0
30
2.98
10
0
0
20
3.13
11
0
0
7
3.25
12
0
0
1
3.33
Total
2
0
94
Other information about this loop
Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,4],[0,5,6,6],[0,7,1,0],[1,8,9,1],[2,9,9,8],[2,7,7,2],[3,6,6,8],[4,7,5,9],[4,8,5,5]]
PD code (use to draw this loop with SnapPy): [[9,20,10,1],[11,8,12,9],[19,4,20,5],[10,2,11,1],[7,12,8,13],[5,15,6,14],[3,18,4,19],[2,18,3,17],[13,17,14,16],[6,15,7,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-17,-2)(8,5,-9,-6)(4,9,-5,-10)(11,2,-12,-3)(3,12,-4,-13)(13,10,-14,-11)(14,19,-15,-20)(20,15,-1,-16)(6,17,-7,-18)(18,7,-19,-8)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16)(-2,11,-14,-20,-16)(-3,-13,-11)(-4,-10,13)(-5,8,-19,14,10)(-6,-18,-8)(-7,18)(-9,4,12,2,-17,6)(-12,3)(-15,20)(1,15,19,7,17)(5,9)
Loop annotated with half-edges
12^1_147 annotated with half-edges