- Minimal pinning sets
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning data
- Pinning number of this multiloop: 5
- Total number of pinning sets: 84
- of which optimal: 4
- of which minimal: 5
- The mean region-degree (mean-degree) of a pinning set is
- on average over all pinning sets: 2.97951
- on average over minimal pinning sets: 2.61333
- on average over optimal pinning sets: 2.6
Refined data for the minimal pinning sets
| Pin label |
Pin color |
Regions |
Cardinality |
Degree sequence |
Mean-degree |
| A (optimal) |
• |
{1, 3, 4, 6, 7} |
5 |
[2, 2, 3, 3, 3] |
2.60 |
| B (optimal) |
• |
{1, 3, 4, 8, 9} |
5 |
[2, 2, 3, 3, 3] |
2.60 |
| C (optimal) |
• |
{1, 2, 4, 8, 9} |
5 |
[2, 2, 3, 3, 3] |
2.60 |
| D (optimal) |
• |
{1, 3, 4, 7, 8} |
5 |
[2, 2, 3, 3, 3] |
2.60 |
| a (minimal) |
• |
{1, 2, 4, 6, 7, 9} |
6 |
[2, 2, 3, 3, 3, 3] |
2.67 |
Data for pinning sets in each cardinal
| Cardinality |
Optimal pinning sets |
Minimal suboptimal pinning sets |
Nonminimal pinning sets |
Averaged mean-degree |
| 5 |
4 |
0 |
0 |
2.6 |
| 6 |
0 |
1 |
17 |
2.81 |
| 7 |
0 |
0 |
30 |
2.98 |
| 8 |
0 |
0 |
23 |
3.1 |
| 9 |
0 |
0 |
8 |
3.17 |
| 10 |
0 |
0 |
1 |
3.2 |
| Total |
4 |
1 |
79 |
|
Other information about this multiloop
Properties
- Region degree sequence: [2, 2, 3, 3, 3, 3, 3, 3, 5, 5]
- Minimal region degree: 2
- Is multisimple: No
Combinatorial encoding data
- Plantri embedding: [[1,2,2,3],[0,4,5,2],[0,1,5,0],[0,6,7,7],[1,7,6,5],[1,4,6,2],[3,5,4,7],[3,6,4,3]]
- PD code (use to draw this multiloop with SnapPy): [[6,16,1,7],[7,14,8,15],[15,5,16,6],[1,12,2,11],[3,13,4,14],[8,4,9,5],[12,9,13,10],[2,10,3,11]]
- Permutation representation (action on half-edges):
- Vertex permutation (15,2,-16,-3)(12,3,-13,-4)(8,5,-9,-6)(1,10,-2,-11)(14,11,-15,-12)(4,13,-5,-14)(9,16,-10,-7)(6,7,-1,-8)
- Edge permutation (-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)
- Face permutation (-1,-11,14,-5,8)(-2,15,11)(-3,12,-15)(-4,-14,-12)(-6,-8)(-7,6,-9)(-10,1,7)(-13,4)(-16,9,5,13,3)(2,10,16)
Multiloop annotated with half-edges