$12^{2}_{153}$ - Minimal pinning sets
Pinning sets for 12^2_153 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_153 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, 7, 11}
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, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,7,7],[0,8,1,0],[1,9,9,5],[1,4,6,6],[2,5,5,9],[2,8,8,2],[3,7,7,9],[4,8,6,4]]
PD code (use to draw this multiloop with SnapPy): [[16,9,1,10],[10,8,11,7],[15,4,16,5],[8,1,9,2],[11,17,12,20],[6,19,7,20],[5,19,6,18],[3,14,4,15],[2,14,3,13],[17,13,18,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,1,-13,-2)(4,7,-5,-8)(13,6,-14,-7)(9,20,-10,-17)(10,15,-11,-16)(16,11,-1,-12)(5,14,-6,-15)(17,2,-18,-3)(3,18,-4,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12)(-2,17,-10,-16,-12)(-3,-19,-9,-17)(-4,-8,19)(-5,-15,10,20,8)(-6,13,1,11,15)(-7,4,18,2,-13)(-11,16)(-14,5,7)(-18,3)(-20,9)(6,14)
Multiloop annotated with half-edges
12^2_153 annotated with half-edges