$11^{2}_{45}$ - Minimal pinning sets
Pinning sets for 11^2_45 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_45 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 128
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: 2.89692
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, 3, 5, 6}
4
[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
4
1
0
0
2.0
5
0
0
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,6,6],[0,6,7,7],[0,7,7,8],[0,8,5,5],[1,4,4,8],[1,8,2,1],[2,3,3,2],[3,6,5,4]]
PD code (use to draw this multiloop with SnapPy): [[12,18,1,13],[13,3,14,4],[15,11,16,12],[17,9,18,10],[1,6,2,7],[7,2,8,3],[14,5,15,4],[10,16,11,17],[5,8,6,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,12,-6,-1)(18,1,-13,-2)(2,13,-3,-14)(11,4,-12,-5)(3,6,-4,-7)(16,7,-17,-8)(14,9,-15,-10)(8,15,-9,-16)(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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,-11,-5)(-2,-14,-10,-18)(-3,-7,16,-9,14)(-4,11,17,7)(-6,3,13,1)(-8,-16)(-12,5)(-13,2)(-15,8,-17,10)(4,6,12)(9,15)
Multiloop annotated with half-edges
11^2_45 annotated with half-edges