$12^{2}_{29}$ - Minimal pinning sets
Pinning sets for 12^2_29 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_29 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, 3, 4, 7, 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, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,5,6],[0,6,7,8],[1,8,8,1],[2,8,7,2],[2,9,9,3],[3,9,9,5],[3,5,4,4],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[14,20,1,15],[15,13,16,14],[19,5,20,6],[1,10,2,11],[12,16,13,17],[6,18,7,19],[9,4,10,5],[2,8,3,7],[11,18,12,17],[3,8,4,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(15,2,-16,-3)(4,13,-5,-14)(14,5,-1,-6)(12,7,-13,-8)(17,10,-18,-11)(9,18,-10,-19)(19,8,-20,-9)(3,20,-4,-15)(11,16,-12,-17)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,15,-4,-14,-6)(-3,-15)(-5,14)(-7,12,16,2)(-8,19,-10,17,-12)(-9,-19)(-11,-17)(-13,4,20,8)(-16,11,-18,9,-20,3)(1,5,13,7)(10,18)
Multiloop annotated with half-edges
12^2_29 annotated with half-edges