$10^{2}_{5}$ - Minimal pinning sets
Pinning sets for 10^2_5 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_5 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 64
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.8189
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 5}
4
[2, 2, 2, 2]
2.00
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
2.0
5
0
0
6
2.4
6
0
0
15
2.67
7
0
0
20
2.86
8
0
0
15
3.0
9
0
0
6
3.11
10
0
0
1
3.2
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 4, 4, 4, 4, 4, 4]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,6,7,7],[0,7,7,6],[0,6,5,5],[1,4,4,1],[1,4,3,2],[2,3,3,2]]
PD code (use to draw this multiloop with SnapPy): [[8,16,1,9],[9,3,10,4],[13,7,14,8],[15,5,16,6],[1,12,2,11],[2,10,3,11],[4,12,5,13],[6,14,7,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-9,-2)(14,3,-15,-4)(12,5,-13,-6)(8,9,-1,-10)(10,7,-11,-8)(2,11,-3,-12)(4,13,-5,-14)(6,15,-7,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,-7,10)(-2,-12,-6,-16)(-3,14,-5,12)(-4,-14)(-8,-10)(-9,8,-11,2)(-13,4,-15,6)(1,9)(3,11,7,15)(5,13)
Multiloop annotated with half-edges
10^2_5 annotated with half-edges