$12^{2}_{155}$ - Minimal pinning sets
Pinning sets for 12^2_155 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_155 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 64
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: 2.85421
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, 4, 6, 9}
6
[2, 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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 4, 4, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,5,6,6],[0,7,7,0],[1,8,8,1],[1,9,9,2],[2,9,7,2],[3,6,8,3],[4,7,9,4],[5,8,6,5]]
PD code (use to draw this multiloop with SnapPy): [[11,16,12,1],[5,10,6,11],[15,20,16,17],[12,2,13,1],[9,4,10,5],[6,18,7,17],[19,14,20,15],[2,14,3,13],[3,8,4,9],[18,8,19,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(4,17,-5,-18)(16,5,-1,-6)(2,7,-3,-8)(10,15,-11,-16)(18,11,-19,-12)(8,13,-9,-14)(14,9,-15,-10)(12,19,-13,-20)(20,3,-17,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,-8,-14,-10,-16,-6)(-3,20,-13,8)(-4,-18,-12,-20)(-5,16,-11,18)(-7,2)(-9,14)(-15,10)(-17,4)(-19,12)(1,5,17,3,7)(9,13,19,11,15)
Multiloop annotated with half-edges
12^2_155 annotated with half-edges