$12^{1}_{299}$ - Minimal pinning sets
Pinning sets for 12^1_299 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_299 Pinning data
Pinning number of this loop: 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, 2, 3, 4, 6, 7}
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 loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 4, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,5,3],[0,2,6,7],[1,7,8,1],[2,8,8,2],[3,8,9,9],[3,9,9,4],[4,6,5,5],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[7,20,8,1],[19,6,20,7],[8,16,9,15],[1,15,2,14],[5,18,6,19],[16,10,17,9],[2,11,3,12],[4,13,5,14],[17,10,18,11],[3,13,4,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (17,4,-18,-5)(7,14,-8,-15)(15,8,-16,-9)(20,9,-1,-10)(10,1,-11,-2)(2,11,-3,-12)(12,19,-13,-20)(13,6,-14,-7)(3,16,-4,-17)(5,18,-6,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10)(-2,-12,-20,-10)(-3,-17,-5,-19,12)(-4,17)(-6,13,19)(-7,-15,-9,20,-13)(-8,15)(-11,2)(-14,7)(-16,3,11,1,9)(-18,5)(4,16,8,14,6,18)
Loop annotated with half-edges
12^1_299 annotated with half-edges