$12^{2}_{129}$ - Minimal pinning sets
Pinning sets for 12^2_129 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_129 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, 9, 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, 4, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,7],[0,7,8,4],[1,3,5,1],[2,4,9,9],[2,9,9,8],[2,8,8,3],[3,7,7,6],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[7,14,8,1],[13,6,14,7],[8,15,9,20],[1,4,2,5],[5,12,6,13],[15,12,16,11],[9,17,10,18],[3,19,4,20],[2,19,3,18],[16,10,17,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(11,4,-12,-5)(19,8,-20,-9)(9,18,-10,-19)(3,10,-4,-11)(5,12,-6,-13)(7,20,-8,-15)(15,14,-16,-1)(1,16,-2,-17)(17,6,-18,-7)
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,-7,-15)(-2,13,-6,17)(-3,-11,-5,-13)(-4,11)(-8,19,-10,3,-14,15)(-9,-19)(-12,5)(-16,1)(-18,9,-20,7)(2,16,14)(4,10,18,6,12)(8,20)
Multiloop annotated with half-edges
12^2_129 annotated with half-edges