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