$11^{2}_{44}$ - Minimal pinning sets
Pinning sets for 11^2_44 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_44 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, 8}
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: [[1,2,2,3],[0,4,4,5],[0,5,6,0],[0,6,7,7],[1,7,5,1],[1,4,8,2],[2,8,8,3],[3,8,4,3],[5,7,6,6]]
PD code (use to draw this multiloop with SnapPy): [[5,14,6,1],[9,4,10,5],[13,6,14,7],[1,15,2,18],[3,8,4,9],[10,8,11,7],[12,15,13,16],[2,17,3,18],[11,17,12,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(10,3,-11,-4)(4,7,-5,-8)(14,5,-1,-6)(2,11,-3,-12)(15,8,-16,-9)(13,16,-14,-17)(17,12,-18,-13)(9,18,-10,-15)
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,-12,17,-14,-6)(-3,10,18,12)(-4,-8,15,-10)(-5,14,16,8)(-7,4,-11,2)(-9,-15)(-13,-17)(-16,13,-18,9)(1,5,7)(3,11)
Multiloop annotated with half-edges
11^2_44 annotated with half-edges