$12^{1}_{297}$ - Minimal pinning sets
Pinning sets for 12^1_297 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_297 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, 3, 7, 11}
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, 4, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,5,6],[0,7,8,0],[1,8,5,1],[2,4,6,6],[2,5,5,7],[3,6,9,9],[3,9,9,4],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[7,20,8,1],[15,6,16,7],[16,19,17,20],[8,2,9,1],[5,14,6,15],[18,13,19,14],[17,13,18,12],[2,12,3,11],[9,4,10,5],[3,10,4,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(12,3,-13,-4)(20,7,-1,-8)(8,19,-9,-20)(9,14,-10,-15)(15,10,-16,-11)(2,11,-3,-12)(13,16,-14,-17)(4,17,-5,-18)(18,5,-19,-6)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,-19,8)(-2,-12,-4,-18,-6)(-3,12)(-5,18)(-7,20,-9,-15,-11,2)(-8,-20)(-10,15)(-13,-17,4)(-14,9,19,5,17)(-16,13,3,11)(1,7)(10,14,16)
Loop annotated with half-edges
12^1_297 annotated with half-edges