$12^{1}_{150}$ - Minimal pinning sets
Pinning sets for 12^1_150 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_150 Pinning data
Pinning number of this loop: 7
Total number of pinning sets: 32
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: 2.80821
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)
• {2, 3, 4, 5, 6, 9, 11}
7
[2, 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
7
1
0
0
2.0
8
0
0
5
2.4
9
0
0
10
2.71
10
0
0
10
2.96
11
0
0
5
3.16
12
0
0
1
3.33
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 7, 9]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,5,1],[2,6,7,2],[3,8,6,3],[4,5,8,7],[4,6,9,9],[5,9,9,6],[7,8,8,7]]
PD code (use to draw this loop with SnapPy): [[20,9,1,10],[10,19,11,20],[8,1,9,2],[18,11,19,12],[2,7,3,8],[12,17,13,18],[13,6,14,7],[3,14,4,15],[5,16,6,17],[4,16,5,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(17,2,-18,-3)(15,4,-16,-5)(13,6,-14,-7)(18,9,-19,-10)(10,19,-11,-20)(20,11,-1,-12)(7,12,-8,-13)(5,14,-6,-15)(3,16,-4,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,12)(-2,17,-4,15,-6,13,-8)(-3,-17)(-5,-15)(-7,-13)(-9,18,2)(-10,-20,-12,7,-14,5,-16,3,-18)(-11,20)(-19,10)(1,11,19,9)(4,16)(6,14)
Loop annotated with half-edges
12^1_150 annotated with half-edges