$12^{2}_{152}$ - Minimal pinning sets
Pinning sets for 12^2_152 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_152 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, 3, 4, 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, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,7,7],[0,7,1,0],[1,8,8,5],[1,4,9,9],[2,9,9,8],[2,8,3,2],[4,7,6,4],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[4,20,1,5],[5,19,6,18],[3,9,4,10],[19,1,20,2],[6,14,7,13],[17,12,18,13],[10,16,11,15],[8,2,9,3],[14,8,15,7],[11,16,12,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (15,2,-16,-3)(20,3,-5,-4)(19,10,-20,-11)(4,5,-1,-6)(13,8,-14,-9)(9,18,-10,-19)(11,6,-12,-7)(7,12,-8,-13)(14,17,-15,-18)(1,16,-2,-17)
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,-17,14,8,12,6)(-2,15,17)(-3,20,10,18,-15)(-4,-6,11,-20)(-5,4)(-7,-13,-9,-19,-11)(-8,13)(-10,19)(-12,7)(-14,-18,9)(-16,1,5,3)(2,16)
Multiloop annotated with half-edges
12^2_152 annotated with half-edges