$11^{2}_{74}$ - Minimal pinning sets
Pinning sets for 11^2_74 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_74 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 168
of which optimal: 3
of which minimal: 8
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.01171
on average over minimal pinning sets: 2.6
on average over optimal pinning sets: 2.6
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {3, 5, 6, 8, 10}
5
[2, 2, 2, 3, 4]
2.60
B (optimal)
• {2, 3, 5, 7, 8}
5
[2, 2, 2, 3, 4]
2.60
C (optimal)
• {3, 4, 5, 8, 9}
5
[2, 2, 2, 3, 4]
2.60
a (minimal)
• {1, 3, 5, 7, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
b (minimal)
• {2, 3, 5, 6, 8, 9}
6
[2, 2, 2, 4, 4, 4]
3.00
c (minimal)
• {3, 4, 5, 7, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
d (minimal)
• {1, 3, 4, 5, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
e (minimal)
• {1, 3, 4, 5, 7, 8}
6
[2, 2, 2, 3, 3, 3]
2.50
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
2.6
6
0
5
18
2.76
7
0
0
52
2.95
8
0
0
53
3.08
9
0
0
28
3.17
10
0
0
8
3.23
11
0
0
1
3.27
Total
3
5
160
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,5],[0,5,6,3],[0,2,7,8],[0,8,8,1],[1,6,2,1],[2,5,7,7],[3,6,6,8],[3,7,4,4]]
PD code (use to draw this multiloop with SnapPy): [[7,12,8,1],[6,18,7,13],[11,4,12,5],[8,4,9,3],[1,14,2,13],[17,5,18,6],[10,16,11,17],[9,16,10,15],[2,14,3,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (1,6,-2,-7)(9,2,-10,-3)(16,3,-17,-4)(5,10,-6,-11)(14,7,-15,-8)(8,15,-9,-16)(4,17,-5,-18)(18,11,-13,-12)(12,13,-1,-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,-7,14)(-2,9,15,7)(-3,16,-9)(-4,-18,-12,-14,-8,-16)(-5,-11,18)(-6,1,13,11)(-10,5,17,3)(-13,12)(-15,8)(-17,4)(2,6,10)
Multiloop annotated with half-edges
11^2_74 annotated with half-edges