$10^{2}_{14}$ - Minimal pinning sets
Pinning sets for 10^2_14 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_14 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 94
of which optimal: 1
of which minimal: 5
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90502
on average over minimal pinning sets: 2.53
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 5, 9}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 2, 5, 9, 10}
5
[2, 2, 2, 3, 3]
2.40
b (minimal)
• {1, 2, 5, 7, 9}
5
[2, 2, 2, 3, 4]
2.60
c (minimal)
• {1, 2, 5, 6, 9}
5
[2, 2, 2, 3, 4]
2.60
d (minimal)
• {1, 2, 4, 5, 9}
5
[2, 2, 2, 3, 5]
2.80
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.25
5
0
4
6
2.58
6
0
0
25
2.8
7
0
0
30
2.95
8
0
0
20
3.06
9
0
0
7
3.14
10
0
0
1
3.2
Total
1
4
89
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,4,0],[0,4,4,5],[0,5,6,1],[1,7,2,2],[2,7,6,3],[3,5,7,7],[4,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[12,16,1,13],[13,11,14,12],[5,15,6,16],[1,10,2,11],[14,4,15,5],[6,9,7,10],[2,7,3,8],[8,3,9,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(13,2,-14,-3)(12,5,-1,-6)(4,7,-5,-8)(11,8,-12,-9)(16,9,-13,-10)(3,14,-4,-15)(10,15,-11,-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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,13,9,-12,-6)(-3,-15,10,-13)(-4,-8,11,15)(-5,12,8)(-7,4,14,2)(-9,16,-11)(-10,-16)(-14,3)(1,5,7)
Multiloop annotated with half-edges
10^2_14 annotated with half-edges