$4^{2}_{1}$ - Minimal pinning sets
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning data
- Pinning number of this multiloop: 4
- Total number of pinning sets: 1
- 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: 2.0
- 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, 4} |
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 |
| Total |
1 |
0 |
0 |
|
Other information about this multiloop
Properties
- Region degree sequence: [2, 2, 2, 2]
- Minimal region degree: 2
- Is multisimple: Yes
Combinatorial encoding data
- Plantri embedding: [[1,1,1,1],[0,0,0,0]]
- PD code (use to draw this multiloop with SnapPy): [[1,4,2,3],[3,2,4,1]]
- Permutation representation (action on half-edges):
- Vertex permutation $\sigma=$ (4,1,-3,-2)(2,3,-1,-4)
- Edge permutation $\epsilon=$ (-1,1)(-2,2)(-3,3)(-4,4)
- Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4)(-2,-4)(-3,2)(1,3)
Multiloop annotated with half-edges