$11^{3}_{8}$ - Minimal pinning sets
Pinning sets for 11^3_8 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^3_8 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, 6, 10}
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, 3, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,4,0],[0,4,4,5],[0,6,7,1],[1,8,2,2],[2,8,6,6],[3,5,5,7],[3,6,8,8],[4,7,7,5]]
PD code (use to draw this multiloop with SnapPy): [[10,14,1,11],[11,9,12,10],[5,13,6,14],[1,8,2,9],[12,4,13,5],[6,15,7,18],[7,17,8,18],[2,17,3,16],[3,15,4,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (15,2,-16,-3)(9,6,-10,-7)(18,7,-15,-8)(3,16,-4,-17)(8,17,-9,-18)(11,10,-12,-1)(5,12,-6,-13)(13,4,-14,-5)(1,14,-2,-11)
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,-11)(-2,15,7,-10,11)(-3,-17,8,-15)(-4,13,-6,9,17)(-5,-13)(-7,18,-9)(-8,-18)(-12,5,-14,1)(-16,3)(2,14,4,16)(6,12,10)
Multiloop annotated with half-edges
11^3_8 annotated with half-edges