$11^{1}_{60}$ - Minimal pinning sets
Pinning sets for 11^1_60 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_60 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 140
of which optimal: 3
of which minimal: 5
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.97754
on average over minimal pinning sets: 2.50667
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, 4, 7, 8}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {1, 2, 4, 5, 8}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
• {1, 2, 4, 7, 10}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {1, 2, 4, 5, 9, 10}
6
[2, 2, 2, 3, 3, 4]
2.67
b (minimal)
• {1, 2, 4, 5, 6, 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
3
0
0
2.4
6
0
2
16
2.69
7
0
0
40
2.9
8
0
0
44
3.05
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
3
2
135
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,5,6],[0,6,7,4],[0,3,7,5],[1,4,2,1],[2,8,8,3],[3,8,8,4],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[8,15,9,16],[17,14,18,15],[10,5,11,6],[1,6,2,7],[16,7,17,8],[4,13,5,14],[11,3,12,2],[12,3,13,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,9,-1,-10)(10,1,-11,-2)(8,3,-9,-4)(17,4,-18,-5)(14,5,-15,-6)(2,11,-3,-12)(15,12,-16,-13)(6,13,-7,-14)(7,16,-8,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10)(-2,-12,15,5,-18,-10)(-3,8,16,12)(-4,17,-8)(-5,14,-7,-17)(-6,-14)(-9,18,4)(-11,2)(-13,6,-15)(-16,7,13)(1,9,3,11)
Loop annotated with half-edges
11^1_60 annotated with half-edges