$11^{1}_{46}$ - Minimal pinning sets
Pinning sets for 11^1_46 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_46 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90403
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 6, 10}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 4, 5, 10}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.2
6
0
0
11
2.55
7
0
0
25
2.79
8
0
0
30
2.97
9
0
0
20
3.1
10
0
0
7
3.2
11
0
0
1
3.27
Total
2
0
94
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,3],[0,2,6,7],[1,7,7,5],[2,4,8,8],[3,8,8,7],[3,6,4,4],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[18,11,1,12],[12,17,13,18],[13,10,14,11],[1,14,2,15],[16,5,17,6],[9,4,10,5],[2,8,3,7],[15,7,16,6],[3,8,4,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(13,2,-14,-3)(3,12,-4,-13)(4,17,-5,-18)(18,5,-1,-6)(10,7,-11,-8)(15,8,-16,-9)(16,11,-17,-12)(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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,13,-4,-18,-6)(-3,-13)(-5,18)(-7,10,14,2)(-8,15,-10)(-9,-15)(-11,16,8)(-12,3,-14,9,-16)(-17,4,12)(1,5,17,11,7)
Loop annotated with half-edges
11^1_46 annotated with half-edges