$12^{2}_{125}$ - Minimal pinning sets
Pinning sets for 12^2_125 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_125 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, 2, 5, 6, 9}
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, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,4,5,6],[0,7,7,4],[1,3,2,1],[2,8,6,6],[2,5,5,9],[3,9,8,3],[5,7,9,9],[6,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[9,16,10,1],[15,8,16,9],[10,14,11,13],[1,6,2,7],[7,14,8,15],[11,17,12,20],[12,19,13,20],[5,2,6,3],[17,5,18,4],[18,3,19,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (17,16,-18,-1)(1,20,-2,-17)(14,3,-15,-4)(12,5,-13,-6)(10,7,-11,-8)(4,11,-5,-12)(6,13,-7,-14)(2,15,-3,-16)(9,18,-10,-19)(19,8,-20,-9)
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,-17)(-2,-16,17)(-3,14,-7,10,18,16)(-4,-12,-6,-14)(-5,12)(-8,19,-10)(-9,-19)(-11,4,-15,2,20,8)(-13,6)(-18,9,-20,1)(3,15)(5,11,7,13)
Multiloop annotated with half-edges
12^2_125 annotated with half-edges