$12^{1}_{240}$ - Minimal pinning sets
Pinning sets for 12^1_240 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_240 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 128
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: 2.90623
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, 11}
5
[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
5
1
0
0
2.0
6
0
0
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,6],[0,6,6,7],[1,8,8,5],[2,4,9,9],[2,9,3,3],[3,9,8,8],[4,7,7,4],[5,7,6,5]]
PD code (use to draw this loop with SnapPy): [[5,20,6,1],[19,4,20,5],[6,4,7,3],[1,10,2,11],[13,18,14,19],[7,14,8,15],[9,2,10,3],[11,16,12,17],[17,12,18,13],[8,16,9,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,20,-8,-1)(1,4,-2,-5)(17,2,-18,-3)(19,8,-20,-9)(15,10,-16,-11)(5,12,-6,-13)(13,6,-14,-7)(9,14,-10,-15)(11,16,-12,-17)(3,18,-4,-19)
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,-5,-13,-7)(-2,17,-12,5)(-3,-19,-9,-15,-11,-17)(-4,1,-8,19)(-6,13)(-10,15)(-14,9,-20,7)(-16,11)(-18,3)(2,4,18)(6,12,16,10,14)(8,20)
Loop annotated with half-edges
12^1_240 annotated with half-edges