$11^{1}_{95}$ - Minimal pinning sets
Pinning sets for 11^1_95 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_95 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 222
of which optimal: 8
of which minimal: 9
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.0631
on average over minimal pinning sets: 2.73333
on average over optimal pinning sets: 2.7
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 5, 9, 11}
5
[2, 2, 3, 3, 3]
2.60
B (optimal)
• {1, 2, 7, 9, 11}
5
[2, 2, 3, 3, 4]
2.80
C (optimal)
• {1, 2, 5, 6, 11}
5
[2, 2, 3, 3, 3]
2.60
D (optimal)
• {1, 2, 6, 8, 11}
5
[2, 2, 3, 3, 4]
2.80
E (optimal)
• {1, 2, 6, 7, 11}
5
[2, 2, 3, 3, 4]
2.80
F (optimal)
• {1, 2, 5, 9, 10}
5
[2, 2, 3, 3, 3]
2.60
G (optimal)
• {1, 2, 6, 10, 11}
5
[2, 2, 3, 3, 3]
2.60
H (optimal)
• {1, 2, 4, 9, 10}
5
[2, 2, 3, 3, 4]
2.80
a (minimal)
• {1, 2, 4, 8, 9, 11}
6
[2, 2, 3, 3, 4, 4]
3.00
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
2.7
6
0
1
37
2.9
7
0
0
69
3.04
8
0
0
64
3.13
9
0
0
33
3.2
10
0
0
9
3.24
11
0
0
1
3.27
Total
8
1
213
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],[0,5,5,6],[0,6,7,3],[0,2,8,4],[0,3,8,5],[1,4,8,1],[1,7,7,2],[2,6,6,8],[3,7,5,4]]
PD code (use to draw this loop with SnapPy): [[18,9,1,10],[10,6,11,5],[17,14,18,15],[8,13,9,14],[1,13,2,12],[6,12,7,11],[4,15,5,16],[16,3,17,4],[7,2,8,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,18,-6,-1)(14,1,-15,-2)(3,8,-4,-9)(16,7,-17,-8)(9,4,-10,-5)(10,17,-11,-18)(6,11,-7,-12)(15,12,-16,-13)(2,13,-3,-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)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14,-3,-9,-5)(-2,-14)(-4,9)(-6,-12,15,1)(-7,16,12)(-8,3,13,-16)(-10,-18,5)(-11,6,18)(-13,2,-15)(-17,10,4,8)(7,11,17)
Loop annotated with half-edges
11^1_95 annotated with half-edges