$11^{1}_{94}$ - Minimal pinning sets
Pinning sets for 11^1_94 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_94 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 288
of which optimal: 4
of which minimal: 6
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.06019
on average over minimal pinning sets: 2.65
on average over optimal pinning sets: 2.625
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 10}
4
[2, 2, 3, 3]
2.50
B (optimal)
• {1, 4, 8, 10}
4
[2, 2, 3, 4]
2.75
C (optimal)
• {1, 3, 4, 10}
4
[2, 2, 3, 3]
2.50
D (optimal)
• {1, 4, 9, 10}
4
[2, 2, 3, 4]
2.75
a (minimal)
• {1, 2, 3, 6, 10}
5
[2, 2, 3, 3, 3]
2.60
b (minimal)
• {1, 3, 5, 6, 10}
5
[2, 2, 3, 3, 4]
2.80
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
4
0
0
2.62
5
0
2
22
2.82
6
0
0
61
2.96
7
0
0
85
3.07
8
0
0
70
3.14
9
0
0
34
3.2
10
0
0
9
3.24
11
0
0
1
3.27
Total
4
2
282
Other information about this loop Properties
Region degree sequence: [2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,6,2],[0,1,6,7],[0,7,7,8],[0,8,5,5],[1,4,4,6],[1,5,8,2],[2,8,3,3],[3,7,6,4]]
PD code (use to draw this loop with SnapPy): [[18,7,1,8],[8,3,9,4],[4,17,5,18],[6,11,7,12],[1,14,2,15],[15,2,16,3],[9,16,10,17],[5,13,6,12],[13,10,14,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,18,-14,-1)(6,1,-7,-2)(16,5,-17,-6)(11,8,-12,-9)(4,9,-5,-10)(10,3,-11,-4)(17,12,-18,-13)(7,14,-8,-15)(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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,-17,-13)(-2,-16,-6)(-3,10,-5,16)(-4,-10)(-7,-15,2)(-8,11,3,15)(-9,4,-11)(-12,17,5,9)(-14,7,1)(-18,13)(8,14,18,12)
Loop annotated with half-edges
11^1_94 annotated with half-edges