$12^{2}_{282}$ - Minimal pinning sets
Pinning sets for 12^2_282
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_282
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, 4, 7, 8, 9, 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, 3, 4, 4, 7, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,5,1],[2,6,7,2],[3,8,6,3],[4,5,9,9],[4,9,8,8],[5,7,7,9],[6,8,7,6]]
PD code (use to draw this multiloop with SnapPy): [[8,20,1,9],[9,7,10,8],[19,1,20,2],[6,10,7,11],[2,18,3,19],[11,5,12,6],[12,17,13,18],[3,16,4,15],[4,14,5,15],[16,13,17,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,8,-10,-1)(19,2,-20,-3)(17,4,-18,-5)(1,20,-2,-9)(14,11,-15,-12)(7,12,-8,-13)(13,6,-14,-7)(10,15,-11,-16)(5,16,-6,-17)(3,18,-4,-19)
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)(-2,19,-4,17,-6,13,-8,9)(-3,-19)(-5,-17)(-7,-13)(-10,-16,5,-18,3,-20,1)(-11,14,6,16)(-12,7,-14)(-15,10,8,12)(2,20)(4,18)(11,15)
Multiloop annotated with half-edges
12^2_282 annotated with half-edges