$11^{1}_{75}$ - Minimal pinning sets
Pinning sets for 11^1_75 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_75 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, 3, 6, 8}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 2, 3, 4, 5, 8}
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, 3, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,5,3],[0,2,6,6],[0,7,8,8],[1,8,2,1],[3,7,7,3],[4,6,6,8],[4,7,5,4]]
PD code (use to draw this loop with SnapPy): [[5,18,6,1],[4,15,5,16],[17,14,18,15],[6,14,7,13],[1,11,2,10],[16,3,17,4],[7,12,8,13],[11,8,12,9],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,18,-14,-1)(8,5,-9,-6)(17,6,-18,-7)(7,16,-8,-17)(4,9,-5,-10)(10,3,-11,-4)(14,11,-15,-12)(1,12,-2,-13)(2,15,-3,-16)
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,-13)(-2,-16,7,-18,13)(-3,10,-5,8,16)(-4,-10)(-6,17,-8)(-7,-17)(-9,4,-11,14,18,6)(-12,1,-14)(-15,2,12)(3,15,11)(5,9)
Loop annotated with half-edges
11^1_75 annotated with half-edges