$7^{1}_{2}$ - Minimal pinning sets
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning data
- Pinning number of this loop: 3
- Total number of pinning sets: 16
- 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: 2.55982
- 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, 4, 6} |
3 |
[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 |
| 3 |
1 |
0 |
0 |
2.0 |
| 4 |
0 |
0 |
4 |
2.38 |
| 5 |
0 |
0 |
6 |
2.6 |
| 6 |
0 |
0 |
4 |
2.75 |
| 7 |
0 |
0 |
1 |
2.86 |
| Total |
1 |
0 |
15 |
|
Other information about this loop
Properties
- Region degree sequence: [2, 2, 2, 3, 3, 4, 4]
- Minimal region degree: 2
- Is multisimple: No
Combinatorial encoding data
- Plantri embedding: [[1,1,2,3],[0,3,2,0],[0,1,4,4],[0,4,4,1],[2,3,3,2]]
- PD code (use to draw this loop with SnapPy): [[5,10,6,1],[9,4,10,5],[6,4,7,3],[1,8,2,9],[7,2,8,3]]
- Permutation representation (action on half-edges):
- Vertex permutation $\sigma=$ (10,3,-1,-4)(6,1,-7,-2)(8,5,-9,-6)(2,7,-3,-8)(4,9,-5,-10)
- Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)(-9,9)(-10,10)
- Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,-9,4)(-2,-8,-6)(-3,10,-5,8)(-4,-10)(-7,2)(1,3,7)(5,9)
Loop annotated with half-edges