$12^{2}_{201}$ - Minimal pinning sets
Pinning sets for 12^2_201 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_201 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 344
of which optimal: 1
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.04482
on average over minimal pinning sets: 2.50417
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 6, 11}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 3, 4, 5, 11}
5
[2, 2, 2, 3, 4]
2.60
b (minimal)
• {1, 2, 3, 4, 7, 11}
6
[2, 2, 2, 3, 3, 3]
2.50
c (minimal)
• {1, 2, 3, 4, 8, 11}
6
[2, 2, 2, 3, 3, 4]
2.67
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
2.25
5
0
1
8
2.58
6
0
2
34
2.79
7
0
0
78
2.95
8
0
0
99
3.07
9
0
0
76
3.17
10
0
0
35
3.24
11
0
0
9
3.29
12
0
0
1
3.33
Total
1
3
340
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,3],[0,2,6,4],[1,3,6,7],[2,7,8,6],[3,5,8,4],[4,9,9,5],[5,9,9,6],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,9,12,10],[12,19,13,20],[1,13,2,14],[14,8,15,9],[6,18,7,19],[2,7,3,8],[15,5,16,6],[17,3,18,4],[4,16,5,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,10,-12,-1)(19,2,-20,-3)(9,4,-10,-5)(18,5,-19,-6)(15,6,-16,-7)(8,17,-9,-18)(1,20,-2,-11)(3,12,-4,-13)(16,13,-17,-14)(7,14,-8,-15)
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,-11)(-2,19,5,-10,11)(-3,-13,16,6,-19)(-4,9,17,13)(-5,18,-9)(-6,15,-8,-18)(-7,-15)(-12,3,-20,1)(-14,7,-16)(-17,8,14)(2,20)(4,12,10)
Multiloop annotated with half-edges
12^2_201 annotated with half-edges