$10^{2}_{2}$ - Minimal pinning sets
Pinning sets for 10^2_2 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_2 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 16
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: 2.71339
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, 6, 7}
6
[2, 2, 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
6
1
0
0
2.0
7
0
0
4
2.43
8
0
0
6
2.75
9
0
0
4
3.0
10
0
0
1
3.2
Total
1
0
15
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,6,1],[2,6,5,2],[3,4,7,7],[3,7,7,4],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[8,16,1,9],[9,7,10,8],[15,1,16,2],[6,10,7,11],[2,14,3,15],[11,3,12,4],[13,5,14,6],[12,5,13,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,9,-1,-10)(10,1,-11,-2)(14,3,-15,-4)(12,5,-13,-6)(16,7,-9,-8)(2,15,-3,-16)(6,11,-7,-12)(4,13,-5,-14)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10)(-2,-16,-8,-10)(-3,14,-5,12,-7,16)(-4,-14)(-6,-12)(-9,8)(-11,6,-13,4,-15,2)(1,9,7,11)(3,15)(5,13)
Multiloop annotated with half-edges
10^2_2 annotated with half-edges