$10^{2}_{26}$ - Minimal pinning sets
Pinning sets for 10^2_26 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_26 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 155
of which optimal: 1
of which minimal: 11
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.08498
on average over minimal pinning sets: 2.97727
on average over optimal pinning sets: 2.75
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, 3, 3, 3]
2.75
a (minimal)
• {2, 5, 6, 8, 10}
5
[2, 3, 3, 3, 4]
3.00
b (minimal)
• {2, 5, 6, 7, 10}
5
[2, 3, 3, 3, 4]
3.00
c (minimal)
• {1, 2, 5, 6, 10}
5
[2, 3, 3, 3, 3]
2.80
d (minimal)
• {2, 4, 5, 9, 10}
5
[2, 3, 3, 3, 4]
3.00
e (minimal)
• {2, 4, 5, 7, 10}
5
[2, 3, 3, 4, 4]
3.20
f (minimal)
• {2, 4, 5, 6, 10}
5
[2, 3, 3, 3, 4]
3.00
g (minimal)
• {2, 3, 5, 7, 10}
5
[2, 3, 3, 3, 4]
3.00
h (minimal)
• {2, 3, 5, 7, 9}
5
[2, 3, 3, 3, 4]
3.00
i (minimal)
• {2, 3, 4, 5, 9}
5
[2, 3, 3, 3, 4]
3.00
j (minimal)
• {2, 3, 5, 6, 8, 9}
6
[2, 3, 3, 3, 3, 4]
3.00
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
2.75
5
0
9
6
2.96
6
0
1
44
3.04
7
0
0
53
3.11
8
0
0
31
3.15
9
0
0
9
3.19
10
0
0
1
3.2
Total
1
10
144
Other information about this multiloop Properties
Region degree sequence: [2, 3, 3, 3, 3, 3, 3, 4, 4, 4]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,2],[0,1,5,6],[0,6,6,7],[0,7,5,1],[1,4,7,2],[2,7,3,3],[3,6,5,4]]
PD code (use to draw this multiloop with SnapPy): [[4,16,1,5],[5,12,6,13],[13,3,14,4],[15,8,16,9],[1,11,2,12],[6,2,7,3],[14,10,15,9],[10,7,11,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,4,-6,-1)(12,1,-13,-2)(14,7,-15,-8)(8,13,-9,-14)(3,10,-4,-11)(16,11,-5,-12)(2,15,-3,-16)(9,6,-10,-7)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-5)(-2,-16,-12)(-3,-11,16)(-4,5,11)(-6,9,13,1)(-7,14,-9)(-8,-14)(-10,3,15,7)(-13,8,-15,2)(4,10,6)
Multiloop annotated with half-edges
10^2_26 annotated with half-edges