$10^{2}_{13}$ - Minimal pinning sets
Pinning sets for 10^2_13 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_13 Pinning data
Pinning number of this multiloop: 3
Total number of pinning sets: 128
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: 2.88583
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, 5, 9}
3
[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
3
1
0
0
2.0
4
0
0
7
2.43
5
0
0
21
2.69
6
0
0
35
2.86
7
0
0
35
2.98
8
0
0
21
3.07
9
0
0
7
3.14
10
0
0
1
3.2
Total
1
0
127
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,4,0],[0,4,5,6],[0,6,7,1],[1,5,5,2],[2,4,4,7],[2,7,7,3],[3,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[6,16,1,7],[7,5,8,6],[15,12,16,13],[1,4,2,5],[8,14,9,13],[9,14,10,15],[3,11,4,12],[2,11,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,2,-6,-3)(14,3,-15,-4)(7,6,-8,-1)(1,8,-2,-9)(12,9,-13,-10)(10,15,-11,-16)(16,11,-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,-9,12,-7)(-2,5,13,9)(-3,14,-5)(-4,-14)(-6,7,11,15,3)(-8,1)(-10,-16,-12)(-11,16)(-13,4,-15,10)(2,8,6)
Multiloop annotated with half-edges
10^2_13 annotated with half-edges