$12^{2}_{118}$ - Minimal pinning sets
Pinning sets for 12^2_118 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_118 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, 4, 6, 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, 3, 3, 3, 8, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,5,0],[0,4,1,1],[1,3,6,6],[2,7,8,2],[4,9,9,4],[5,9,8,8],[5,7,7,9],[6,8,7,6]]
PD code (use to draw this multiloop with SnapPy): [[3,10,4,1],[2,20,3,11],[9,4,10,5],[1,12,2,11],[12,19,13,20],[5,8,6,9],[18,13,19,14],[15,7,16,8],[6,16,7,17],[14,17,15,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,2,-8,-3)(16,5,-17,-6)(3,6,-4,-7)(1,8,-2,-9)(19,14,-20,-15)(4,17,-5,-18)(15,18,-16,-19)(13,20,-14,-11)(10,11,-1,-12)(12,9,-13,-10)
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,-9,12)(-2,7,-4,-18,15,-20,13,9)(-3,-7)(-5,16,18)(-6,3,-8,1,11,-14,19,-16)(-10,-12)(-11,10,-13)(-15,-19)(-17,4,6)(2,8)(5,17)(14,20)
Multiloop annotated with half-edges
12^2_118 annotated with half-edges