$11^{1}_{80}$ - Minimal pinning sets
Pinning sets for 11^1_80 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_80 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 124
of which optimal: 5
of which minimal: 5
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90811
on average over minimal pinning sets: 2.32
on average over optimal pinning sets: 2.32
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 4, 6}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 4, 6, 8}
5
[2, 2, 2, 2, 3]
2.20
C (optimal)
• {1, 2, 4, 6, 9}
5
[2, 2, 2, 2, 4]
2.40
D (optimal)
• {1, 2, 4, 6, 11}
5
[2, 2, 2, 2, 3]
2.20
E (optimal)
• {1, 2, 4, 6, 10}
5
[2, 2, 2, 2, 5]
2.60
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
5
0
0
2.32
6
0
0
20
2.65
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
5
0
119
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: [[1,2,3,3],[0,4,5,5],[0,6,6,7],[0,7,8,0],[1,8,8,5],[1,4,6,1],[2,5,7,2],[2,6,8,3],[3,7,4,4]]
PD code (use to draw this loop with SnapPy): [[18,13,1,14],[14,10,15,9],[4,17,5,18],[12,1,13,2],[10,7,11,8],[15,8,16,9],[16,3,17,4],[5,3,6,2],[6,11,7,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,18,-14,-1)(7,4,-8,-5)(12,5,-13,-6)(6,11,-7,-12)(3,8,-4,-9)(15,10,-16,-11)(1,14,-2,-15)(9,16,-10,-17)(17,2,-18,-3)
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,-11,6,-13)(-2,17,-10,15)(-3,-9,-17)(-4,7,11,-16,9)(-5,12,-7)(-6,-12)(-8,3,-18,13,5)(-14,1)(2,14,18)(4,8)(10,16)
Loop annotated with half-edges
11^1_80 annotated with half-edges