$11^{2}_{39}$ - Minimal pinning sets
Pinning sets for 11^2_39 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_39 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90403
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 5, 6, 10}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 5, 6, 10}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.2
6
0
0
11
2.55
7
0
0
25
2.79
8
0
0
30
2.97
9
0
0
20
3.1
10
0
0
7
3.2
11
0
0
1
3.27
Total
2
0
94
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,6,6,7],[0,7,7,4],[0,3,7,8],[1,8,8,1],[1,8,2,2],[2,4,3,3],[4,6,5,5]]
PD code (use to draw this multiloop with SnapPy): [[10,18,1,11],[11,7,12,8],[15,9,16,10],[3,17,4,18],[1,4,2,5],[6,12,7,13],[8,14,9,15],[16,2,17,3],[5,14,6,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,10,-12,-1)(9,2,-10,-3)(14,5,-15,-6)(18,7,-11,-8)(16,3,-17,-4)(6,17,-7,-18)(1,12,-2,-13)(8,13,-9,-14)(4,15,-5,-16)
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,-13,8,-11)(-2,9,13)(-3,16,-5,14,-9)(-4,-16)(-6,-18,-8,-14)(-7,18)(-10,11,7,17,3)(-12,1)(-15,4,-17,6)(2,12,10)(5,15)
Multiloop annotated with half-edges
11^2_39 annotated with half-edges