$11^{1}_{98}$ - Minimal pinning sets
Pinning sets for 11^1_98 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_98 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 184
of which optimal: 1
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97765
on average over minimal pinning sets: 2.4625
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 7, 10}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 2, 3, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
b (minimal)
• {1, 3, 5, 6, 10}
5
[2, 2, 2, 3, 4]
2.60
c (minimal)
• {1, 3, 6, 9, 10}
5
[2, 2, 2, 3, 4]
2.60
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
2.25
5
0
3
7
2.56
6
0
0
33
2.79
7
0
0
54
2.96
8
0
0
50
3.08
9
0
0
27
3.16
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
3
180
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,6],[0,6,6,7],[0,7,7,4],[0,3,8,1],[1,8,8,6],[1,5,2,2],[2,8,3,3],[4,7,5,5]]
PD code (use to draw this loop with SnapPy): [[5,18,6,1],[15,4,16,5],[17,8,18,9],[6,13,7,14],[1,14,2,15],[3,10,4,11],[16,10,17,9],[12,7,13,8],[2,12,3,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,1,-13,-2)(9,4,-10,-5)(14,5,-15,-6)(6,13,-7,-14)(18,7,-1,-8)(8,17,-9,-18)(3,10,-4,-11)(16,11,-17,-12)(2,15,-3,-16)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-17,8)(-2,-16,-12)(-3,-11,16)(-4,9,17,11)(-5,14,-7,18,-9)(-6,-14)(-8,-18)(-10,3,15,5)(-13,6,-15,2)(1,7,13)(4,10)
Loop annotated with half-edges
11^1_98 annotated with half-edges