$12^{2}_{271}$ - Minimal pinning sets
Pinning sets for 12^2_271 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_271 Pinning data
Pinning number of this multiloop: 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, 6, 7}
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 multiloop 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],[2,4,9,9],[2,9,9,7],[3,6,8,8],[3,7,7,4],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[14,5,1,6],[6,15,7,20],[13,19,14,20],[4,1,5,2],[15,8,16,7],[16,12,17,13],[18,10,19,11],[2,10,3,9],[3,8,4,9],[11,17,12,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(4,15,-5,-16)(14,5,-1,-6)(6,13,-7,-14)(18,7,-19,-8)(16,9,-17,-10)(1,12,-2,-13)(8,17,-9,-18)(10,19,-11,-20)(20,3,-15,-4)
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,-13,6)(-2,11,19,7,13)(-3,20,-11)(-4,-16,-10,-20)(-5,14,-7,18,-9,16)(-6,-14)(-8,-18)(-12,1,5,15,3)(-15,4)(-17,8,-19,10)(2,12)(9,17)
Multiloop annotated with half-edges
12^2_271 annotated with half-edges