$10^{3}_{3}$ - Minimal pinning sets
Pinning sets for 10^3_3 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^3_3 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, 3, 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, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,6],[0,6,6,0],[0,7,4,4],[1,3,3,5],[1,4,7,7],[1,7,2,2],[3,6,5,5]]
PD code (use to draw this multiloop with SnapPy): [[6,12,1,7],[7,3,8,4],[11,5,12,6],[1,13,2,16],[2,15,3,16],[8,15,9,14],[4,10,5,11],[13,10,14,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,1,-15,-2)(12,3,-13,-4)(16,9,-11,-10)(2,11,-3,-12)(4,13,-5,-14)(6,7,-1,-8)(8,5,-9,-6)(10,15,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14,-5,8)(-2,-12,-4,-14)(-3,12)(-6,-8)(-7,6,-9,16)(-10,-16)(-11,2,-15,10)(-13,4)(1,7,15)(3,11,9,5,13)
Multiloop annotated with half-edges
10^3_3 annotated with half-edges