$11^{1}_{62}$ - Minimal pinning sets
Pinning sets for 11^1_62 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_62 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90403
on average over minimal pinning sets: 2.2
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
B (optimal)
• {1, 2, 4, 5, 8}
5
[2, 2, 2, 2, 3]
2.20
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
2.2
6
0
0
11
2.55
7
0
0
25
2.79
8
0
0
30
2.97
9
0
0
20
3.1
10
0
0
7
3.2
11
0
0
1
3.27
Total
2
0
94
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,7,7,8],[0,8,8,4],[0,3,8,5],[1,4,6,1],[1,5,7,7],[2,6,6,2],[2,4,3,3]]
PD code (use to draw this loop with SnapPy): [[7,18,8,1],[6,13,7,14],[17,10,18,11],[8,3,9,4],[1,4,2,5],[14,5,15,6],[15,12,16,13],[11,16,12,17],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(17,2,-18,-3)(12,3,-13,-4)(18,7,-1,-8)(15,8,-16,-9)(13,10,-14,-11)(4,11,-5,-12)(9,14,-10,-15)(5,16,-6,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,16,8)(-2,17,-6)(-3,12,-5,-17)(-4,-12)(-7,18,2)(-8,15,-10,13,3,-18)(-9,-15)(-11,4,-13)(-14,9,-16,5,11)(1,7)(10,14)
Loop annotated with half-edges
11^1_62 annotated with half-edges