$12^{1}_{133}$ - Minimal pinning sets
Pinning sets for 12^1_133 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_133 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, 5, 7}
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, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,6],[0,7,3,0],[0,2,4,4],[1,3,3,8],[1,8,6,6],[1,5,5,9],[2,9,9,8],[4,7,9,5],[6,8,7,7]]
PD code (use to draw this loop with SnapPy): [[7,20,8,1],[3,6,4,7],[19,8,20,9],[1,19,2,18],[2,17,3,18],[5,12,6,13],[4,12,5,11],[9,15,10,14],[16,13,17,14],[10,15,11,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (19,2,-20,-3)(15,4,-16,-5)(7,20,-8,-1)(1,8,-2,-9)(12,9,-13,-10)(10,5,-11,-6)(6,11,-7,-12)(18,13,-19,-14)(14,17,-15,-18)(3,16,-4,-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,-9,12,-7)(-2,19,13,9)(-3,-17,14,-19)(-4,15,17)(-5,10,-13,18,-15)(-6,-12,-10)(-8,1)(-11,6)(-14,-18)(-16,3,-20,7,11,5)(2,8,20)(4,16)
Loop annotated with half-edges
12^1_133 annotated with half-edges