$12^{2}_{286}$ - Minimal pinning sets
Pinning sets for 12^2_286 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_286 Pinning data
Pinning number of this multiloop: 7
Total number of pinning sets: 32
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: 2.80821
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, 4, 5, 6, 9}
7
[2, 2, 2, 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
7
1
0
0
2.0
8
0
0
5
2.4
9
0
0
10
2.71
10
0
0
10
2.96
11
0
0
5
3.16
12
0
0
1
3.33
Total
1
0
31
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 4, 4, 5, 5, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,6],[0,6,7,7],[1,5,5,1],[2,4,4,8],[2,8,3,2],[3,9,9,3],[5,9,9,6],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[8,20,1,9],[9,7,10,8],[12,19,13,20],[1,18,2,17],[6,10,7,11],[11,5,12,6],[18,13,19,14],[2,16,3,17],[4,14,5,15],[15,3,16,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,8,-10,-1)(17,2,-18,-3)(15,4,-16,-5)(12,19,-13,-20)(1,20,-2,-9)(7,10,-8,-11)(11,6,-12,-7)(18,13,-19,-14)(5,14,-6,-15)(3,16,-4,-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,-9)(-2,17,-4,15,-6,11,-8,9)(-3,-17)(-5,-15)(-7,-11)(-10,7,-12,-20,1)(-13,18,2,20)(-14,5,-16,3,-18)(-19,12,6,14)(4,16)(8,10)(13,19)
Multiloop annotated with half-edges
12^2_286 annotated with half-edges