$12^{1}_{119}$ - Minimal pinning sets
Pinning sets for 12^1_119 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_119 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 128
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: 2.90623
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, 4, 7, 9}
5
[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
5
1
0
0
2.0
6
0
0
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 6, 7]
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],[1,3,7,8],[2,9,9,6],[2,5,7,7],[4,6,6,8],[4,7,9,9],[5,8,8,5]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[15,2,16,3],[19,4,20,5],[1,14,2,15],[16,14,17,13],[5,11,6,10],[18,9,19,10],[17,9,18,8],[12,7,13,8],[11,7,12,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-17,-2)(3,8,-4,-9)(9,4,-10,-5)(5,14,-6,-15)(15,6,-16,-7)(7,2,-8,-3)(10,13,-11,-14)(18,11,-19,-12)(20,17,-1,-18)(12,19,-13,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,6,14,-11,18)(-2,7,-16)(-3,-9,-5,-15,-7)(-4,9)(-6,15)(-8,3)(-10,-14,5)(-12,-20,-18)(-13,10,4,8,2,-17,20)(-19,12)(1,17)(11,13,19)
Loop annotated with half-edges
12^1_119 annotated with half-edges