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