$11^{1}_{35}$ - Minimal pinning sets
Pinning sets for 11^1_35 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_35 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 128
of which optimal: 1
of which minimal: 8
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.99582
on average over minimal pinning sets: 2.55417
on average over optimal pinning sets: 2.6
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {2, 4, 5, 8, 10}
5
[2, 2, 2, 3, 4]
2.60
a (minimal)
• {2, 4, 6, 7, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
b (minimal)
• {2, 3, 6, 7, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
c (minimal)
• {2, 3, 5, 6, 8, 10}
6
[2, 2, 2, 3, 3, 4]
2.67
d (minimal)
• {1, 2, 4, 7, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
e (minimal)
• {1, 2, 3, 4, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
f (minimal)
• {1, 2, 3, 6, 8, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
g (minimal)
• {2, 3, 6, 8, 9, 10}
6
[2, 2, 2, 3, 3, 4]
2.67
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
2.6
6
0
7
6
2.67
7
0
0
36
2.89
8
0
0
43
3.05
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
7
120
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,6],[0,6,7,3],[0,2,7,7],[0,8,8,1],[1,8,8,6],[1,5,7,2],[2,6,3,3],[4,5,5,4]]
PD code (use to draw this loop with SnapPy): [[5,18,6,1],[4,9,5,10],[14,17,15,18],[6,15,7,16],[1,11,2,10],[12,3,13,4],[13,8,14,9],[16,7,17,8],[11,3,12,2]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,18,-10,-1)(13,4,-14,-5)(10,5,-11,-6)(1,6,-2,-7)(7,16,-8,-17)(3,12,-4,-13)(11,14,-12,-15)(2,15,-3,-16)(17,8,-18,-9)
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,-7,-17,-9)(-2,-16,7)(-3,-13,-5,10,18,8,16)(-4,13)(-6,1,-10)(-8,17)(-11,-15,2,6)(-12,3,15)(-14,11,5)(-18,9)(4,12,14)
Loop annotated with half-edges
11^1_35 annotated with half-edges