$12^{2}_{337}$ - Minimal pinning sets
Pinning sets for 12^2_337 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_337 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 256
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: 2.96564
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}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,5],[0,5,6,0],[0,6,7,4],[1,3,8,1],[1,8,9,2],[2,9,9,3],[3,9,8,8],[4,7,7,5],[5,7,6,6]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,5,12,6],[19,9,20,10],[1,14,2,13],[4,12,5,13],[6,18,7,19],[8,14,9,15],[2,16,3,17],[17,3,18,4],[7,16,8,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,10,-12,-1)(15,2,-16,-3)(13,6,-14,-7)(1,16,-2,-17)(17,8,-18,-9)(5,18,-6,-19)(19,4,-20,-5)(9,20,-10,-11)(3,12,-4,-13)(7,14,-8,-15)
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,-9,-11)(-2,15,-8,17)(-3,-13,-7,-15)(-4,19,-6,13)(-5,-19)(-10,11)(-12,3,-16,1)(-14,7)(-18,5,-20,9)(2,16)(4,12,10,20)(6,18,8,14)
Multiloop annotated with half-edges
12^2_337 annotated with half-edges