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