$10^{3}_{2}$ - Minimal pinning sets
Pinning sets for 10^3_2 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^3_2 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, 3, 5, 10}
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, 3, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,7,1,1],[1,7,7,5],[2,4,6,6],[2,5,5,7],[3,6,4,4]]
PD code (use to draw this multiloop with SnapPy): [[3,8,4,1],[2,12,3,9],[7,4,8,5],[1,10,2,9],[11,16,12,13],[5,16,6,15],[6,14,7,15],[10,14,11,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,2,-6,-3)(1,6,-2,-7)(8,9,-1,-10)(10,7,-11,-8)(4,13,-5,-14)(14,3,-15,-4)(12,15,-9,-16)(16,11,-13,-12)
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,-7,10)(-2,5,13,11,7)(-3,14,-5)(-4,-14)(-6,1,9,15,3)(-8,-10)(-9,8,-11,16)(-12,-16)(-13,4,-15,12)(2,6)
Multiloop annotated with half-edges
10^3_2 annotated with half-edges