$12^{1}_{306}$ - Minimal pinning sets
Pinning sets for 12^1_306 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_306 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, 6, 7, 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 loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 4, 4, 5, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,5,6],[0,7,7,0],[1,5,5,1],[2,4,4,8],[2,9,9,7],[3,6,8,3],[5,7,9,9],[6,8,8,6]]
PD code (use to draw this loop with SnapPy): [[20,15,1,16],[16,8,17,7],[19,6,20,7],[14,1,15,2],[8,18,9,17],[9,18,10,19],[12,5,13,6],[2,13,3,14],[10,3,11,4],[4,11,5,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(15,2,-16,-3)(3,12,-4,-13)(20,7,-1,-8)(18,9,-19,-10)(16,11,-17,-12)(13,4,-14,-5)(5,14,-6,-15)(10,17,-11,-18)(6,19,-7,-20)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8)(-2,15,-6,-20,-8)(-3,-13,-5,-15)(-4,13)(-7,20)(-9,18,-11,16,2)(-10,-18)(-12,3,-16)(-14,5)(-17,10,-19,6,14,4,12)(1,7,19,9)(11,17)
Loop annotated with half-edges
12^1_306 annotated with half-edges