$11^{2}_{58}$ - Minimal pinning sets
Pinning sets for 11^2_58 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_58 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, 3, 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, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,5,5,6],[0,7,7,4],[1,3,8,8],[1,8,2,2],[2,8,7,7],[3,6,6,3],[4,6,5,4]]
PD code (use to draw this multiloop with SnapPy): [[14,18,1,15],[15,13,16,14],[17,9,18,10],[1,7,2,6],[12,5,13,6],[16,11,17,10],[8,3,9,4],[7,3,8,2],[4,11,5,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,5,-1,-6)(6,1,-7,-2)(10,3,-11,-4)(4,13,-5,-14)(16,7,-17,-8)(8,15,-9,-16)(2,9,-3,-10)(18,11,-15,-12)(12,17,-13,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,-10,-4,-14,-6)(-3,10)(-5,14)(-7,16,-9,2)(-8,-16)(-11,18,-13,4)(-12,-18)(-15,8,-17,12)(1,5,13,17,7)(3,9,15,11)
Multiloop annotated with half-edges
11^2_58 annotated with half-edges