$12^{2}_{70}$ - Minimal pinning sets
Pinning sets for 12^2_70 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_70 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 256
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: 2.96564
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, 11}
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
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,2,0],[0,1,4,5],[0,6,7,1],[2,7,8,8],[2,8,6,6],[3,5,5,9],[3,9,9,4],[4,9,5,4],[6,8,7,7]]
PD code (use to draw this multiloop with SnapPy): [[16,9,1,10],[10,15,11,16],[11,8,12,9],[1,14,2,15],[7,20,8,17],[12,6,13,5],[13,4,14,5],[2,18,3,17],[19,6,20,7],[3,18,4,19]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(3,10,-4,-11)(19,4,-20,-5)(9,6,-10,-7)(14,7,-15,-8)(15,12,-16,-13)(8,13,-9,-14)(17,16,-18,-1)(1,18,-2,-19)(5,20,-6,-17)
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)(-17,17)(-18,18)(-19,19)(-20,20)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,-19,-5,-17)(-2,11,-4,19)(-3,-11)(-6,9,13,-16,17)(-7,14,-9)(-8,-14)(-10,3,-12,15,7)(-13,8,-15)(-18,1)(-20,5)(2,18,16,12)(4,10,6,20)
Multiloop annotated with half-edges
12^2_70 annotated with half-edges