$11^{2}_{57}$ - Minimal pinning sets
Pinning sets for 11^2_57 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_57 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 64
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: 2.83846
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, 4, 6, 10}
5
[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
5
1
0
0
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,5,5,3],[0,2,6,6],[1,6,7,7],[1,8,2,2],[3,8,4,3],[4,8,8,4],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[14,18,1,15],[15,13,16,14],[7,17,8,18],[1,8,2,9],[3,12,4,13],[16,6,17,7],[2,10,3,9],[11,4,12,5],[5,10,6,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,14,-8,-1)(15,2,-16,-3)(11,4,-12,-5)(5,12,-6,-13)(1,6,-2,-7)(13,8,-14,-9)(18,9,-15,-10)(3,16,-4,-17)(10,17,-11,-18)
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)(-2,15,9,-14,7)(-3,-17,10,-15)(-4,11,17)(-5,-13,-9,18,-11)(-6,1,-8,13)(-10,-18)(-12,5)(-16,3)(2,6,12,4,16)(8,14)
Multiloop annotated with half-edges
11^2_57 annotated with half-edges