$11^{2}_{73}$ - Minimal pinning sets
Pinning sets for 11^2_73 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_73 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 128
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: 2.98309
on average over minimal pinning sets: 2.475
on average over optimal pinning sets: 2.46667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 8, 9}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {1, 2, 3, 6, 9}
5
[2, 2, 2, 3, 4]
2.60
C (optimal)
• {1, 2, 3, 4, 9}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {1, 2, 3, 7, 8, 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
3
0
0
2.47
6
0
1
15
2.72
7
0
0
35
2.9
8
0
0
40
3.04
9
0
0
25
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
3
1
124
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: [[1,2,3,4],[0,4,5,2],[0,1,5,3],[0,2,6,7],[0,8,8,1],[1,6,6,2],[3,5,5,7],[3,6,8,8],[4,7,7,4]]
PD code (use to draw this multiloop with SnapPy): [[7,12,8,1],[6,18,7,13],[11,17,12,18],[8,17,9,16],[1,14,2,13],[10,5,11,6],[9,5,10,4],[15,3,16,4],[14,3,15,2]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,13,-1,-14)(14,1,-15,-2)(2,7,-3,-8)(8,3,-9,-4)(5,10,-6,-11)(15,6,-16,-7)(9,16,-10,-17)(4,17,-5,-18)(18,11,-13,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14)(-2,-8,-4,-18,-12,-14)(-3,8)(-5,-11,18)(-6,15,1,13,11)(-7,2,-15)(-9,-17,4)(-10,5,17)(-13,12)(-16,9,3,7)(6,10,16)
Multiloop annotated with half-edges
11^2_73 annotated with half-edges