$11^{2}_{47}$ - Minimal pinning sets
Pinning sets for 11^2_47 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_47 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 116
of which optimal: 1
of which minimal: 6
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.98222
on average over minimal pinning sets: 2.53889
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, 5, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {1, 3, 4, 6, 9, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
b (minimal)
• {1, 3, 4, 6, 10, 11}
6
[2, 2, 2, 3, 3, 4]
2.67
c (minimal)
• {1, 2, 4, 6, 9, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
d (minimal)
• {1, 2, 4, 6, 10, 11}
6
[2, 2, 2, 3, 3, 4]
2.67
e (minimal)
• {1, 3, 4, 5, 6, 10}
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
1
0
0
2.4
6
0
5
6
2.62
7
0
0
31
2.86
8
0
0
39
3.03
9
0
0
25
3.15
10
0
0
8
3.22
11
0
0
1
3.27
Total
1
5
110
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,2],[0,1,5,0],[0,6,7,7],[1,8,5,1],[2,4,8,6],[3,5,8,7],[3,6,8,3],[4,7,6,5]]
PD code (use to draw this multiloop with SnapPy): [[6,18,1,7],[7,16,8,17],[17,5,18,6],[1,11,2,12],[15,8,16,9],[4,14,5,15],[10,13,11,14],[2,13,3,12],[9,3,10,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,6,-8,-1)(15,2,-16,-3)(4,9,-5,-10)(10,5,-11,-6)(8,11,-9,-12)(1,12,-2,-13)(17,14,-18,-15)(3,16,-4,-17)(13,18,-14,-7)
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,-13,-7)(-2,15,-18,13)(-3,-17,-15)(-4,-10,-6,7,-14,17)(-5,10)(-8,-12,1)(-9,4,16,2,12)(-11,8,6)(-16,3)(5,9,11)(14,18)
Multiloop annotated with half-edges
11^2_47 annotated with half-edges