$12^{2}_{120}$ - Minimal pinning sets
Pinning sets for 12^2_120 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_120 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, 4, 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, 3, 4, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,4,1,1],[1,3,7,8],[2,8,9,9],[2,9,9,7],[4,6,8,8],[4,7,7,5],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[3,14,4,1],[2,20,3,15],[13,4,14,5],[1,16,2,15],[16,19,17,20],[5,10,6,11],[7,12,8,13],[8,18,9,19],[17,9,18,10],[6,12,7,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(18,7,-19,-8)(3,8,-4,-9)(9,4,-10,-5)(5,10,-6,-11)(1,12,-2,-13)(6,19,-7,-20)(17,20,-18,-15)(14,15,-1,-16)(16,13,-17,-14)
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,-13,16)(-2,11,-6,-20,17,13)(-3,-9,-5,-11)(-4,9)(-7,18,20)(-8,3,-12,1,15,-18)(-10,5)(-14,-16)(-15,14,-17)(-19,6,10,4,8)(2,12)(7,19)
Multiloop annotated with half-edges
12^2_120 annotated with half-edges