$12^{2}_{26}$ - Minimal pinning sets
Pinning sets for 12^2_26 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_26 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, 3, 4, 9, 11}
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, 3, 4, 4, 5, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,4,0],[0,5,6,0],[1,6,6,7],[1,7,8,8],[2,9,9,7],[2,7,3,3],[3,6,5,4],[4,9,9,4],[5,8,8,5]]
PD code (use to draw this multiloop with SnapPy): [[7,12,8,1],[11,6,12,7],[8,2,9,1],[10,20,11,13],[15,5,16,6],[2,18,3,19],[9,14,10,13],[14,19,15,20],[4,16,5,17],[17,3,18,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,1,-13,-2)(18,3,-19,-4)(9,4,-10,-5)(5,10,-6,-11)(11,6,-12,-7)(2,19,-3,-20)(12,13,-1,-14)(17,14,-18,-15)(8,15,-9,-16)(16,7,-17,-8)
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,-3,18,14)(-2,-20)(-4,9,15,-18)(-5,-11,-7,16,-9)(-6,11)(-8,-16)(-10,5)(-12,-14,17,7)(-13,12,6,10,4,-19,2)(-15,8,-17)(1,13)(3,19)
Multiloop annotated with half-edges
12^2_26 annotated with half-edges