$11^{1}_{20}$ - Minimal pinning sets
Pinning sets for 11^1_20 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_20 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 80
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90697
on average over minimal pinning sets: 2.26667
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 5, 10}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 2, 3, 4, 6, 10}
6
[2, 2, 2, 2, 3, 3]
2.33
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
1
0
0
2.2
6
0
1
6
2.5
7
0
0
19
2.74
8
0
0
26
2.94
9
0
0
19
3.09
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
1
78
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],[0,4,5,6],[0,6,7,7],[0,8,8,6],[0,5,5,1],[1,4,4,6],[1,5,3,2],[2,8,8,2],[3,7,7,3]]
PD code (use to draw this loop with SnapPy): [[13,18,14,1],[12,9,13,10],[4,17,5,18],[14,7,15,8],[1,11,2,10],[2,11,3,12],[3,8,4,9],[16,5,17,6],[6,15,7,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,18,-12,-1)(9,2,-10,-3)(16,3,-17,-4)(7,4,-8,-5)(5,14,-6,-15)(15,6,-16,-7)(1,10,-2,-11)(17,12,-18,-13)(8,13,-9,-14)
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)(-2,9,13,-18,11)(-3,16,6,14,-9)(-4,7,-16)(-5,-15,-7)(-6,15)(-8,-14,5)(-10,1,-12,17,3)(-13,8,4,-17)(2,10)(12,18)
Loop annotated with half-edges
11^1_20 annotated with half-edges