$11^{1}_{96}$ - Minimal pinning sets
Pinning sets for 11^1_96 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_96 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 254
of which optimal: 1
of which minimal: 8
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.0667
on average over minimal pinning sets: 2.78333
on average over optimal pinning sets: 2.5
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {2, 4, 7, 10}
4
[2, 2, 3, 3]
2.50
a (minimal)
• {1, 2, 6, 7, 10}
5
[2, 2, 3, 3, 3]
2.60
b (minimal)
• {2, 4, 6, 9, 10}
5
[2, 2, 3, 3, 4]
2.80
c (minimal)
• {2, 5, 6, 9, 10}
5
[2, 2, 3, 4, 4]
3.00
d (minimal)
• {1, 2, 6, 9, 10}
5
[2, 2, 3, 3, 4]
2.80
e (minimal)
• {2, 5, 6, 10, 11}
5
[2, 2, 3, 3, 4]
2.80
f (minimal)
• {1, 2, 6, 10, 11}
5
[2, 2, 3, 3, 3]
2.60
g (minimal)
• {2, 3, 5, 6, 7, 10}
6
[2, 2, 3, 3, 4, 5]
3.17
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
2.5
5
0
6
7
2.75
6
0
1
47
2.93
7
0
0
79
3.06
8
0
0
69
3.14
9
0
0
34
3.2
10
0
0
9
3.24
11
0
0
1
3.27
Total
1
7
246
Other information about this loop Properties
Region degree sequence: [2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,6],[0,6,6,3],[0,2,7,4],[0,3,8,1],[1,8,7,6],[1,5,2,2],[3,5,8,8],[4,7,7,5]]
PD code (use to draw this loop with SnapPy): [[18,5,1,6],[6,15,7,16],[12,17,13,18],[13,4,14,5],[1,14,2,15],[7,10,8,11],[16,11,17,12],[8,3,9,4],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,18,-6,-1)(10,1,-11,-2)(15,2,-16,-3)(17,6,-18,-7)(4,7,-5,-8)(13,8,-14,-9)(16,11,-17,-12)(3,12,-4,-13)(9,14,-10,-15)
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)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10,14,8,-5)(-2,15,-10)(-3,-13,-9,-15)(-4,-8,13)(-6,17,11,1)(-7,4,12,-17)(-11,16,2)(-12,3,-16)(-14,9)(-18,5,7)(6,18)
Loop annotated with half-edges
11^1_96 annotated with half-edges