$12^{1}_{246}$ - Minimal pinning sets
Pinning sets for 12^1_246 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_246 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, 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, 3, 4, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,5],[0,6,7,0],[0,8,4,4],[1,3,3,8],[1,9,6,1],[2,5,7,7],[2,6,6,9],[3,9,9,4],[5,8,8,7]]
PD code (use to draw this loop with SnapPy): [[15,20,16,1],[3,14,4,15],[19,16,20,17],[1,9,2,8],[2,7,3,8],[13,4,14,5],[17,13,18,12],[18,11,19,12],[9,6,10,7],[5,10,6,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(7,4,-8,-5)(20,5,-1,-6)(6,19,-7,-20)(3,8,-4,-9)(16,9,-17,-10)(10,15,-11,-16)(1,12,-2,-13)(17,14,-18,-15)(13,18,-14,-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,-13,-19,6)(-2,11,15,-18,13)(-3,-9,16,-11)(-4,7,19,-14,17,9)(-5,20,-7)(-6,-20)(-8,3,-12,1,5)(-10,-16)(-15,10,-17)(2,12)(4,8)(14,18)
Loop annotated with half-edges
12^1_246 annotated with half-edges