$11^{2}_{65}$ - Minimal pinning sets
Pinning sets for 11^2_65 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_65 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 32
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.78769
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 6, 7, 8}
6
[2, 2, 2, 2, 2, 2]
2.00
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
6
1
0
0
2.0
7
0
0
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 5, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,5,0],[1,6,7,1],[2,8,8,5],[2,4,6,6],[3,5,5,7],[3,6,8,8],[4,7,7,4]]
PD code (use to draw this multiloop with SnapPy): [[12,18,1,13],[13,11,14,12],[17,1,18,2],[10,14,11,15],[2,8,3,7],[16,6,17,7],[15,6,16,5],[9,4,10,5],[8,4,9,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (1,6,-2,-7)(7,2,-8,-3)(3,18,-4,-13)(13,4,-14,-5)(5,12,-6,-1)(16,9,-17,-10)(14,11,-15,-12)(8,17,-9,-18)(10,15,-11,-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,-7,-3,-13,-5)(-2,7)(-4,13)(-6,1)(-8,-18,3)(-9,16,-11,14,4,18)(-10,-16)(-12,5,-14)(-15,10,-17,8,2,6,12)(9,17)(11,15)
Multiloop annotated with half-edges
11^2_65 annotated with half-edges