$12^{2}_{133}$ - Minimal pinning sets
Pinning sets for 12^2_133 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_133 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, 5, 7}
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],[0,6,6,7],[0,8,1,0],[1,8,5,5],[1,4,4,9],[2,9,9,2],[2,9,8,8],[3,7,7,4],[5,7,6,6]]
PD code (use to draw this multiloop with SnapPy): [[14,20,1,15],[15,19,16,18],[13,4,14,5],[19,1,20,2],[16,9,17,8],[17,7,18,8],[5,12,6,13],[3,10,4,11],[2,10,3,9],[11,6,12,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (10,1,-11,-2)(8,3,-9,-4)(15,4,-16,-5)(5,20,-6,-15)(6,13,-7,-14)(14,7,-1,-8)(2,9,-3,-10)(17,12,-18,-13)(16,19,-17,-20)(11,18,-12,-19)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10,-3,8)(-2,-10)(-4,15,-6,-14,-8)(-5,-15)(-7,14)(-9,2,-11,-19,16,4)(-12,17,19)(-13,6,20,-17)(-16,-20,5)(-18,11,1,7,13)(3,9)(12,18)
Multiloop annotated with half-edges
12^2_133 annotated with half-edges