$12^{2}_{280}$ - Minimal pinning sets
Pinning sets for 12^2_280
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_280
Pinning data
Pinning number of this multiloop: 6
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: 2.85421
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, 3, 5, 6, 9, 11}
6
[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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this multiloop
Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 4, 4, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,6,6,7],[0,7,8,0],[1,9,9,1],[1,9,6,6],[2,5,5,2],[2,8,8,3],[3,7,7,9],[4,8,5,4]]
PD code (use to draw this multiloop with SnapPy): [[12,5,1,6],[6,13,7,20],[11,17,12,18],[4,1,5,2],[13,8,14,7],[9,19,10,20],[18,10,19,11],[16,2,17,3],[3,15,4,16],[8,15,9,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(4,19,-5,-20)(16,7,-17,-8)(1,10,-2,-11)(14,11,-15,-12)(12,13,-1,-14)(8,15,-9,-16)(6,17,-7,-18)(18,3,-19,-4)(20,5,-13,-6)
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,-11,14)(-2,9,15,11)(-3,18,-7,16,-9)(-4,-20,-6,-18)(-5,20)(-8,-16)(-10,1,13,5,19,3)(-12,-14)(-13,12,-15,8,-17,6)(-19,4)(2,10)(7,17)
Multiloop annotated with half-edges
12^2_280 annotated with half-edges