$12^{2}_{134}$ - Minimal pinning sets
Pinning sets for 12^2_134 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_134 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, 3, 4, 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, 3, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,4],[0,5,5,6],[0,7,1,0],[1,8,9,1],[2,9,6,2],[2,5,7,7],[3,6,6,8],[4,7,9,9],[4,8,8,5]]
PD code (use to draw this multiloop with SnapPy): [[12,20,1,13],[13,19,14,18],[11,4,12,5],[19,1,20,2],[14,17,15,18],[5,10,6,11],[6,3,7,4],[2,7,3,8],[8,16,9,17],[15,9,16,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(13,4,-14,-5)(12,5,-1,-6)(17,8,-18,-9)(1,10,-2,-11)(6,11,-7,-12)(3,14,-4,-15)(20,15,-13,-16)(16,19,-17,-20)(7,18,-8,-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,-11,6)(-2,9,-18,7,11)(-3,-15,20,-17,-9)(-4,13,15)(-5,12,-7,-19,16,-13)(-6,-12)(-8,17,19)(-10,1,5,-14,3)(-16,-20)(2,10)(4,14)(8,18)
Multiloop annotated with half-edges
12^2_134 annotated with half-edges