$12^{1}_{145}$ - Minimal pinning sets
Pinning sets for 12^1_145 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_145 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, 3, 6, 9}
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, 3, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,7,8],[0,8,1,0],[1,7,9,9],[1,9,6,6],[2,5,5,9],[2,4,8,8],[2,7,7,3],[4,6,5,4]]
PD code (use to draw this loop with SnapPy): [[11,20,12,1],[13,10,14,11],[16,19,17,20],[12,2,13,1],[4,9,5,10],[14,8,15,7],[15,6,16,7],[18,3,19,4],[17,3,18,2],[8,5,9,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (4,1,-5,-2)(11,2,-12,-3)(3,10,-4,-11)(20,5,-1,-6)(9,6,-10,-7)(12,15,-13,-16)(7,16,-8,-17)(17,8,-18,-9)(18,13,-19,-14)(14,19,-15,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4,10,6)(-2,11,-4)(-3,-11)(-5,20,-15,12,2)(-6,9,-18,-14,-20)(-7,-17,-9)(-8,17)(-10,3,-12,-16,7)(-13,18,8,16)(-19,14)(1,5)(13,15,19)
Loop annotated with half-edges
12^1_145 annotated with half-edges