$11^{1}_{6}$ - Minimal pinning sets
Pinning sets for 11^1_6 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_6 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, 3, 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, 4, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,5,6,3],[0,2,1,0],[1,7,7,8],[1,8,8,2],[2,8,7,7],[4,6,6,4],[4,6,5,5]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[11,8,12,9],[17,2,18,3],[10,2,11,1],[7,14,8,15],[12,4,13,3],[5,16,6,17],[15,6,16,7],[13,4,14,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (15,18,-16,-1)(1,10,-2,-11)(11,2,-12,-3)(13,4,-14,-5)(9,6,-10,-7)(5,12,-6,-13)(3,14,-4,-15)(7,16,-8,-17)(17,8,-18,-9)
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,-3,-15)(-2,11)(-4,13,-6,9,-18,15)(-5,-13)(-7,-17,-9)(-8,17)(-10,1,-16,7)(-12,5,-14,3)(2,10,6,12)(4,14)(8,16,18)
Loop annotated with half-edges
11^1_6 annotated with half-edges