$12^{1}_{16}$ - Minimal pinning sets
Pinning sets for 12^1_16 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_16 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 256
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: 2.96564
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, 7, 11}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,4,1,1],[1,3,6,5],[2,4,7,8],[2,8,7,4],[5,6,9,9],[5,9,9,6],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[2,11,3,12],[19,4,20,5],[1,13,2,12],[13,10,14,11],[5,14,6,15],[9,18,10,19],[6,18,7,17],[15,8,16,9],[7,16,8,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (17,2,-18,-3)(13,6,-14,-7)(11,8,-12,-9)(20,9,-1,-10)(10,19,-11,-20)(3,12,-4,-13)(5,14,-6,-15)(15,4,-16,-5)(7,16,-8,-17)(1,18,-2,-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,-19,10)(-2,17,-8,11,19)(-3,-13,-7,-17)(-4,15,-6,13)(-5,-15)(-9,20,-11)(-10,-20)(-12,3,-18,1,9)(-14,5,-16,7)(2,18)(4,12,8,16)(6,14)
Loop annotated with half-edges
12^1_16 annotated with half-edges