$12^{2}_{281}$ - Minimal pinning sets
Pinning sets for 12^2_281 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_281 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, 3, 3, 4, 8, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,6,6,3],[0,2,4,0],[1,3,5,1],[1,4,7,7],[2,8,8,2],[5,9,9,5],[6,9,9,6],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[16,20,1,17],[17,9,18,10],[15,2,16,3],[19,1,20,2],[8,18,9,19],[10,8,11,7],[3,14,4,15],[11,6,12,7],[13,4,14,5],[5,12,6,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,16,-14,-1)(11,2,-12,-3)(9,4,-10,-5)(5,8,-6,-9)(20,7,-17,-8)(3,10,-4,-11)(1,12,-2,-13)(18,15,-19,-16)(14,19,-15,-20)(6,17,-7,-18)
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,-13)(-2,11,-4,9,-6,-18,-16,13)(-3,-11)(-5,-9)(-7,20,-15,18)(-8,5,-10,3,-12,1,-14,-20)(-17,6,8)(-19,14,16)(2,12)(4,10)(7,17)(15,19)
Multiloop annotated with half-edges
12^2_281 annotated with half-edges