$12^{1}_{30}$ - Minimal pinning sets
Pinning sets for 12^1_30 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_30 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, 2, 3, 5, 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, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,2],[0,1,5,0],[0,6,7,4],[1,3,8,1],[2,8,8,6],[3,5,9,9],[3,9,9,8],[4,7,5,5],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[13,20,14,1],[12,15,13,16],[19,14,20,15],[1,10,2,11],[16,11,17,12],[18,5,19,6],[9,4,10,5],[2,8,3,7],[17,7,18,6],[3,8,4,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(15,2,-16,-3)(3,14,-4,-15)(4,19,-5,-20)(20,5,-1,-6)(18,7,-19,-8)(13,8,-14,-9)(16,11,-17,-12)(9,12,-10,-13)(10,17,-11,-18)
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,-20,-6)(-3,-15)(-5,20)(-7,18,-11,16,2)(-8,13,-10,-18)(-9,-13)(-12,9,-14,3,-16)(-17,10,12)(-19,4,14,8)(1,5,19,7)(11,17)
Loop annotated with half-edges
12^1_30 annotated with half-edges