$11^{2}_{46}$ - Minimal pinning sets
Pinning sets for 11^2_46 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_46 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 80
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90697
on average over minimal pinning sets: 2.26667
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, 3, 7, 10}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 2, 3, 5, 6, 10}
6
[2, 2, 2, 2, 3, 3]
2.33
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
1
0
0
2.2
6
0
1
6
2.5
7
0
0
19
2.74
8
0
0
26
2.94
9
0
0
19
3.09
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
1
78
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,2],[0,1,5,6],[0,6,6,0],[1,7,7,5],[1,4,8,2],[2,8,3,3],[4,8,8,4],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[8,18,1,9],[9,14,10,15],[15,7,16,8],[17,1,18,2],[5,13,6,14],[10,6,11,7],[16,3,17,2],[12,4,13,5],[11,4,12,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-17,-2)(11,2,-12,-3)(13,4,-14,-5)(5,12,-6,-13)(6,17,-7,-18)(18,7,-9,-8)(8,9,-1,-10)(15,10,-16,-11)(3,14,-4,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,10)(-2,11,-16)(-3,-15,-11)(-4,13,-6,-18,-8,-10,15)(-5,-13)(-7,18)(-9,8)(-12,5,-14,3)(-17,6,12,2)(1,9,7,17)(4,14)
Multiloop annotated with half-edges
11^2_46 annotated with half-edges