$9^{2}_{5}$ - Minimal pinning sets
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning data
- Pinning number of this multiloop: 4
- Total number of pinning sets: 32
- 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: 2.72966
- 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, 6} |
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 |
5 |
2.4 |
| 6 |
0 |
0 |
10 |
2.67 |
| 7 |
0 |
0 |
10 |
2.86 |
| 8 |
0 |
0 |
5 |
3.0 |
| 9 |
0 |
0 |
1 |
3.11 |
| Total |
1 |
0 |
31 |
|
Other information about this multiloop
Properties
- Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 5, 5]
- Minimal region degree: 2
- Is multisimple: No
Combinatorial encoding data
- Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,6,6,3],[0,2,4,0],[1,3,5,1],[1,4,6,6],[2,5,5,2]]
- PD code (use to draw this multiloop with SnapPy): [[10,14,1,11],[11,6,12,5],[9,2,10,3],[13,1,14,2],[6,13,7,12],[7,4,8,5],[3,8,4,9]]
- Permutation representation (action on half-edges):
- Vertex permutation $\sigma=$ (7,10,-8,-1)(5,2,-6,-3)(3,14,-4,-11)(1,6,-2,-7)(12,9,-13,-10)(8,13,-9,-14)(11,4,-12,-5)
- 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)
- Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-7)(-2,5,-12,-10,7)(-3,-11,-5)(-4,11)(-6,1,-8,-14,3)(-9,12,4,14)(-13,8,10)(2,6)(9,13)
Multiloop annotated with half-edges