$11^{2}_{76}$ - Minimal pinning sets
Pinning sets for 11^2_76 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_76 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 132
of which optimal: 3
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97744
on average over minimal pinning sets: 2.51429
on average over optimal pinning sets: 2.4
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, 3, 3]
2.40
B (optimal)
• {1, 2, 3, 6, 11}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
• {1, 2, 3, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {1, 2, 3, 4, 7, 8, 11}
7
[2, 2, 2, 3, 3, 4, 4]
2.86
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
3
0
0
2.4
6
0
0
16
2.69
7
0
1
35
2.89
8
0
0
42
3.04
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
3
1
128
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,2],[0,1,5,6],[0,7,7,0],[1,7,6,8],[1,8,8,2],[2,8,4,7],[3,6,4,3],[4,6,5,5]]
PD code (use to draw this multiloop with SnapPy): [[7,14,8,1],[6,18,7,15],[13,17,14,18],[8,2,9,1],[15,3,16,4],[12,5,13,6],[16,10,17,11],[2,10,3,9],[4,11,5,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (15,14,-16,-1)(9,2,-10,-3)(6,13,-7,-14)(16,7,-17,-8)(1,8,-2,-9)(4,11,-5,-12)(12,5,-13,-6)(10,17,-11,-18)(3,18,-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,-9,-3,-15)(-2,9)(-4,-12,-6,-14,15)(-5,12)(-7,16,14)(-8,1,-16)(-10,-18,3)(-11,4,18)(-13,6)(-17,10,2,8)(5,11,17,7,13)
Multiloop annotated with half-edges
11^2_76 annotated with half-edges