$12^{2}_{285}$ - Minimal pinning sets
Pinning sets for 12^2_285 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_285 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, 6, 7, 11}
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, 4, 6, 8]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,6,1],[2,6,7,2],[3,8,8,9],[3,9,9,4],[4,9,8,8],[5,7,7,5],[5,7,6,6]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,9,12,10],[19,1,20,2],[8,12,9,13],[2,18,3,19],[13,5,14,6],[17,7,18,8],[3,16,4,15],[4,14,5,15],[6,16,7,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,3,-17,-4)(20,5,-11,-6)(14,7,-15,-8)(12,9,-13,-10)(2,17,-3,-18)(18,1,-19,-2)(4,19,-5,-20)(10,11,-1,-12)(8,13,-9,-14)(6,15,-7,-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)(-17,17)(-18,18)(-19,19)(-20,20)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,-3,16,-7,14,-9,12)(-2,-18)(-4,-20,-6,-16)(-5,20)(-8,-14)(-10,-12)(-11,10,-13,8,-15,6)(-17,2,-19,4)(1,11,5,19)(3,17)(7,15)(9,13)
Multiloop annotated with half-edges
12^2_285 annotated with half-edges