$12^{2}_{17}$ - Minimal pinning sets
Pinning sets for 12^2_17 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_17 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, 5}
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: [[1,2,3,4],[0,5,5,6],[0,6,7,8],[0,8,7,6],[0,6,5,5],[1,4,4,1],[1,4,3,2],[2,3,9,9],[2,9,9,3],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,3,12,4],[15,9,16,10],[19,5,20,6],[1,14,2,13],[2,12,3,13],[4,14,5,15],[8,18,9,19],[16,7,17,6],[17,7,18,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,1,-11,-2)(18,3,-19,-4)(4,15,-5,-16)(16,5,-17,-6)(14,7,-15,-8)(10,11,-1,-12)(12,9,-13,-10)(2,13,-3,-14)(6,17,-7,-18)(8,19,-9,-20)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,20,-9,12)(-2,-14,-8,-20)(-3,18,-7,14)(-4,-16,-6,-18)(-5,16)(-10,-12)(-11,10,-13,2)(-15,4,-19,8)(-17,6)(1,11)(3,13,9,19)(5,15,7,17)
Multiloop annotated with half-edges
12^2_17 annotated with half-edges