$10^{2}_{17}$ - Minimal pinning sets
Pinning sets for 10^2_17 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_17 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 90
of which optimal: 8
of which minimal: 8
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.91579
on average over minimal pinning sets: 2.55
on average over optimal pinning sets: 2.55
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 5, 6, 9}
5
[2, 2, 2, 3, 4]
2.60
B (optimal)
• {1, 3, 4, 5, 9}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
• {1, 3, 5, 7, 9}
5
[2, 2, 2, 3, 4]
2.60
D (optimal)
• {1, 3, 5, 9, 10}
5
[2, 2, 2, 3, 5]
2.80
E (optimal)
• {1, 2, 4, 5, 9}
5
[2, 2, 2, 3, 3]
2.40
F (optimal)
• {1, 2, 5, 8, 9}
5
[2, 2, 2, 3, 4]
2.60
G (optimal)
• {1, 2, 5, 7, 9}
5
[2, 2, 2, 3, 4]
2.60
H (optimal)
• {1, 2, 3, 5, 9}
5
[2, 2, 2, 3, 3]
2.40
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
8
0
0
2.55
6
0
0
24
2.79
7
0
0
30
2.95
8
0
0
20
3.06
9
0
0
7
3.14
10
0
0
1
3.2
Total
8
0
82
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,6,6],[0,7,7,4],[0,3,7,5],[1,4,6,1],[2,5,7,2],[3,6,4,3]]
PD code (use to draw this multiloop with SnapPy): [[7,12,8,1],[6,16,7,13],[11,15,12,16],[8,3,9,4],[1,4,2,5],[13,5,14,6],[14,10,15,11],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(11,2,-12,-3)(14,3,-15,-4)(12,7,-1,-8)(15,8,-16,-9)(5,10,-6,-11)(9,16,-10,-13)(4,13,-5,-14)
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)(-15,15)(-16,16)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,10,16,8)(-2,11,-6)(-3,14,-5,-11)(-4,-14)(-7,12,2)(-8,15,3,-12)(-9,-13,4,-15)(-10,5,13)(-16,9)(1,7)
Multiloop annotated with half-edges
10^2_17 annotated with half-edges