$12^{2}_{36}$ - Minimal pinning sets
Pinning sets for 12^2_36 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_36 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 64
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: 2.85421
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, 6, 8, 9}
6
[2, 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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,6,7,4],[0,4,4,0],[1,3,3,2],[1,8,8,1],[2,8,9,9],[2,9,9,8],[5,7,6,5],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,3,12,4],[17,9,18,10],[19,1,20,2],[2,18,3,19],[12,5,13,4],[6,16,7,17],[8,14,9,15],[5,14,6,13],[15,7,16,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,1,-15,-2)(2,15,-3,-16)(18,5,-19,-6)(20,7,-11,-8)(12,9,-13,-10)(16,3,-17,-4)(6,17,-7,-18)(4,19,-5,-20)(10,11,-1,-12)(8,13,-9,-14)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14,-9,12)(-2,-16,-4,-20,-8,-14)(-3,16)(-5,18,-7,20)(-6,-18)(-10,-12)(-11,10,-13,8)(-15,2)(-17,6,-19,4)(1,11,7,17,3,15)(5,19)(9,13)
Multiloop annotated with half-edges
12^2_36 annotated with half-edges