$11^{2}_{60}$ - Minimal pinning sets
Pinning sets for 11^2_60 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_60 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 48
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: 2.84761
on average over minimal pinning sets: 2.16667
on average over optimal pinning sets: 2.16667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 5, 6, 8, 10}
6
[2, 2, 2, 2, 2, 3]
2.17
B (optimal)
• {1, 2, 4, 5, 8, 10}
6
[2, 2, 2, 2, 2, 3]
2.17
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
6
2
0
0
2.17
7
0
0
9
2.54
8
0
0
16
2.81
9
0
0
14
3.02
10
0
0
6
3.17
11
0
0
1
3.27
Total
2
0
46
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,4,5],[0,6,6,0],[1,7,2,1],[2,8,8,6],[3,5,7,3],[4,6,8,8],[5,7,7,5]]
PD code (use to draw this multiloop with SnapPy): [[10,18,1,11],[11,8,12,7],[9,6,10,7],[17,1,18,2],[8,13,9,12],[15,5,16,6],[2,16,3,17],[13,3,14,4],[4,14,5,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-17,-2)(18,3,-11,-4)(7,4,-8,-5)(5,14,-6,-15)(12,9,-13,-10)(15,6,-16,-7)(2,17,-3,-18)(10,11,-1,-12)(8,13,-9,-14)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,6,14,-9,12)(-2,-18,-4,7,-16)(-3,18)(-5,-15,-7)(-6,15)(-8,-14,5)(-10,-12)(-11,10,-13,8,4)(-17,2)(1,11,3,17)(9,13)
Multiloop annotated with half-edges
11^2_60 annotated with half-edges