$12^{2}_{14}$ - Minimal pinning sets
Pinning sets for 12^2_14 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_14 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, 5, 11}
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, 3, 3, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,5,6,6],[0,7,8,5],[0,5,1,1],[1,4,3,2],[2,8,7,2],[3,6,9,9],[3,9,9,6],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[3,10,4,1],[2,20,3,11],[13,9,14,10],[4,18,5,19],[1,12,2,11],[12,19,13,20],[8,14,9,15],[17,7,18,8],[5,16,6,15],[6,16,7,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(19,4,-20,-5)(8,5,-9,-6)(3,20,-4,-11)(11,10,-12,-1)(1,12,-2,-13)(9,14,-10,-15)(18,15,-19,-16)(7,16,-8,-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,-13,-3,-11)(-2,13)(-4,19,15,-10,11)(-5,8,16,-19)(-6,17,-8)(-7,-17)(-9,-15,18,6)(-12,1)(-14,9,5,-20,3)(-16,7,-18)(2,12,10,14)(4,20)
Multiloop annotated with half-edges
12^2_14 annotated with half-edges