$11^{2}_{36}$ - Minimal pinning sets
Pinning sets for 11^2_36 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_36 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 184
of which optimal: 1
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97765
on average over minimal pinning sets: 2.4625
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 4, 7, 10}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 4, 6, 9, 10}
5
[2, 2, 2, 3, 4]
2.60
b (minimal)
• {1, 2, 4, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
c (minimal)
• {1, 4, 6, 10, 11}
5
[2, 2, 2, 3, 4]
2.60
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.25
5
0
3
7
2.56
6
0
0
33
2.79
7
0
0
54
2.96
8
0
0
50
3.08
9
0
0
27
3.16
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
3
180
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,6,7],[0,7,7,8],[0,8,8,6],[0,6,5,5],[1,4,4,6],[1,5,4,3],[1,8,2,2],[2,7,3,3]]
PD code (use to draw this multiloop with SnapPy): [[6,18,1,7],[7,3,8,4],[15,5,16,6],[17,12,18,13],[1,9,2,10],[10,2,11,3],[8,11,9,12],[4,14,5,15],[16,14,17,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(15,4,-16,-5)(12,5,-13,-6)(3,14,-4,-15)(13,16,-14,-17)(10,17,-11,-18)(18,9,-7,-10)(6,7,-1,-8)(2,11,-3,-12)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8)(-2,-12,-6,-8)(-3,-15,-5,12)(-4,15)(-7,6,-13,-17,10)(-9,18,-11,2)(-10,-18)(-14,3,11,17)(-16,13,5)(1,7,9)(4,14,16)
Multiloop annotated with half-edges
11^2_36 annotated with half-edges