$12^{1}_{157}$ - Minimal pinning sets
Pinning sets for 12^1_157 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_157 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, 3, 4, 5, 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: [[1,1,2,2],[0,3,4,0],[0,4,5,0],[1,6,6,7],[1,7,5,2],[2,4,8,6],[3,5,8,3],[3,9,9,4],[5,9,9,6],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[20,13,1,14],[14,19,15,20],[12,1,13,2],[7,18,8,19],[15,3,16,2],[16,11,17,12],[17,6,18,7],[8,4,9,3],[5,10,6,11],[4,10,5,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(5,20,-6,-1)(1,6,-2,-7)(12,7,-13,-8)(16,9,-17,-10)(3,14,-4,-15)(10,15,-11,-16)(8,17,-9,-18)(18,11,-19,-12)(19,4,-20,-5)
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,-7,12,-19,-5)(-2,13,7)(-3,-15,10,-17,8,-13)(-4,19,11,15)(-6,1)(-8,-18,-12)(-9,16,-11,18)(-10,-16)(-14,3)(-20,5)(2,6,20,4,14)(9,17)
Loop annotated with half-edges
12^1_157 annotated with half-edges