$12^{1}_{28}$ - Minimal pinning sets
Pinning sets for 12^1_28 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_28 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, 5, 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, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,5,6],[0,7,8,8],[1,8,9,1],[2,9,9,2],[2,9,7,7],[3,6,6,8],[3,7,4,3],[4,6,5,5]]
PD code (use to draw this loop with SnapPy): [[5,20,6,1],[19,4,20,5],[6,16,7,15],[1,13,2,12],[3,18,4,19],[16,8,17,7],[9,14,10,15],[13,10,14,11],[2,11,3,12],[17,8,18,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (15,20,-16,-1)(3,12,-4,-13)(13,4,-14,-5)(9,6,-10,-7)(18,7,-19,-8)(8,17,-9,-18)(5,10,-6,-11)(11,2,-12,-3)(19,14,-20,-15)(1,16,-2,-17)
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,-17,8,-19,-15)(-2,11,-6,9,17)(-3,-13,-5,-11)(-4,13)(-7,18,-9)(-8,-18)(-10,5,-14,19,7)(-12,3)(-16,1)(-20,15)(2,16,20,14,4,12)(6,10)
Loop annotated with half-edges
12^1_28 annotated with half-edges