$10^{2}_{21}$ - Minimal pinning sets
Pinning sets for 10^2_21 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_21 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, 6, 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: [[1,2,2,3],[0,4,4,2],[0,1,5,0],[0,5,6,6],[1,6,7,1],[2,7,7,3],[3,7,4,3],[4,6,5,5]]
PD code (use to draw this multiloop with SnapPy): [[5,12,6,1],[4,7,5,8],[11,6,12,7],[1,13,2,16],[8,3,9,4],[10,13,11,14],[2,15,3,16],[9,15,10,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(9,4,-10,-5)(2,5,-3,-6)(3,10,-4,-11)(16,7,-13,-8)(12,13,-1,-14)(14,11,-15,-12)(8,15,-9,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,-3,-11,14)(-2,-6)(-4,9,15,11)(-5,2,-7,16,-9)(-8,-16)(-10,3,5)(-12,-14)(-13,12,-15,8)(1,13,7)(4,10)
Multiloop annotated with half-edges
10^2_21 annotated with half-edges