$10^{2}_{10}$ - Minimal pinning sets
Pinning sets for 10^2_10 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_10 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, 5}
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, 3, 3, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,2,0],[0,1,4,5],[0,6,6,1],[2,7,5,5],[2,4,4,7],[3,7,7,3],[4,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[10,16,1,11],[11,9,12,10],[12,15,13,16],[1,8,2,9],[4,14,5,15],[13,5,14,6],[7,2,8,3],[3,6,4,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,10,-6,-1)(16,3,-11,-4)(1,4,-2,-5)(9,6,-10,-7)(14,7,-15,-8)(2,11,-3,-12)(15,12,-16,-13)(8,13,-9,-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,-5)(-2,-12,15,7,-10,5)(-3,16,12)(-4,1,-6,9,13,-16)(-7,14,-9)(-8,-14)(-11,2,4)(-13,8,-15)(3,11)(6,10)
Multiloop annotated with half-edges
10^2_10 annotated with half-edges