$6^{2}_{1}$ - Minimal pinning sets
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning data
- Pinning number of this multiloop: 4
- Total number of pinning sets: 4
- 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: 2.36667
- 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} |
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 |
2 |
2.4 |
| 6 |
0 |
0 |
1 |
2.67 |
| Total |
1 |
0 |
3 |
|
Other information about this multiloop
Properties
- Region degree sequence: [2, 2, 2, 2, 4, 4]
- Minimal region degree: 2
- Is multisimple: Yes
Combinatorial encoding data
- Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,3,3,0],[1,2,2,1]]
- PD code (use to draw this multiloop with SnapPy): [[4,8,1,5],[5,3,6,4],[7,1,8,2],[2,6,3,7]]
- Permutation representation (action on half-edges):
- Vertex permutation $\sigma=$ (5,4,-6,-1)(7,2,-8,-3)(1,8,-2,-5)(3,6,-4,-7)
- Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)(-5,5)(-6,6)(-7,7)(-8,8)
- Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-5)(-2,7,-4,5)(-3,-7)(-6,3,-8,1)(2,8)(4,6)
Multiloop annotated with half-edges