$11^{1}_{59}$ - Minimal pinning sets
Pinning sets for 11^1_59 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_59 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 120
of which optimal: 2
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97399
on average over minimal pinning sets: 2.45
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, 3, 7, 10}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {2, 3, 7, 10, 11}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {1, 2, 3, 5, 6, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
b (minimal)
• {2, 3, 5, 6, 10, 11}
6
[2, 2, 2, 3, 3, 3]
2.50
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.4
6
0
2
11
2.65
7
0
0
32
2.87
8
0
0
39
3.03
9
0
0
25
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
2
2
116
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,6,3],[0,2,6,6],[0,7,8,8],[1,8,7,1],[2,7,3,3],[4,6,5,8],[4,7,5,4]]
PD code (use to draw this loop with SnapPy): [[5,18,6,1],[13,4,14,5],[14,17,15,18],[6,15,7,16],[1,11,2,10],[3,12,4,13],[16,7,17,8],[11,8,12,9],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(14,5,-15,-6)(9,6,-10,-7)(18,7,-1,-8)(8,17,-9,-18)(1,10,-2,-11)(4,13,-5,-14)(12,15,-13,-16)(3,16,-4,-17)
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,-17,8)(-2,11)(-4,-14,-6,9,17)(-5,14)(-7,18,-9)(-8,-18)(-10,1,7)(-12,-16,3)(-13,4,16)(-15,12,2,10,6)(5,13,15)
Loop annotated with half-edges
11^1_59 annotated with half-edges