$11^{1}_{38}$ - Minimal pinning sets
Pinning sets for 11^1_38 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_38 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 144
of which optimal: 4
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97268
on average over minimal pinning sets: 2.4
on average over optimal pinning sets: 2.4
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 7, 10}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {1, 3, 4, 7, 10}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
• {1, 2, 4, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
D (optimal)
• {1, 3, 4, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
4
0
0
2.4
6
0
0
20
2.7
7
0
0
41
2.91
8
0
0
44
3.05
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
4
0
140
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,4,5],[0,6,3,0],[0,2,7,1],[1,7,8,5],[1,4,8,8],[2,8,7,7],[3,6,6,4],[4,6,5,5]]
PD code (use to draw this loop with SnapPy): [[18,5,1,6],[6,16,7,15],[4,17,5,18],[1,17,2,16],[7,11,8,10],[14,9,15,10],[3,12,4,13],[2,12,3,11],[8,13,9,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (15,2,-16,-3)(11,6,-12,-7)(7,4,-8,-5)(8,17,-9,-18)(18,9,-1,-10)(5,10,-6,-11)(12,3,-13,-4)(13,16,-14,-17)(1,14,-2,-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,-15,-3,12,6,10)(-2,15)(-4,7,-12)(-5,-11,-7)(-6,11)(-8,-18,-10,5)(-9,18)(-13,-17,8,4)(-14,1,9,17)(-16,13,3)(2,14,16)
Loop annotated with half-edges
11^1_38 annotated with half-edges