$10^{2}_{4}$ - Minimal pinning sets
Pinning sets for 10^2_4 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_4 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, 7}
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, 3, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,5,6,3],[0,2,4,0],[1,3,6,1],[1,7,7,2],[2,7,7,4],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[12,16,1,13],[13,7,14,8],[11,2,12,3],[15,1,16,2],[6,14,7,15],[8,4,9,3],[5,10,6,11],[4,10,5,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,12,-10,-1)(1,6,-2,-7)(16,5,-13,-6)(7,2,-8,-3)(3,8,-4,-9)(14,11,-15,-12)(4,13,-5,-14)(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,-7,-3,-9)(-2,7)(-4,-14,-12,9)(-5,16,-11,14)(-6,1,-10,-16)(-8,3)(-13,4,8,2,6)(-15,10,12)(5,13)(11,15)
Multiloop annotated with half-edges
10^2_4 annotated with half-edges