$12^{1}_{125}$ - Minimal pinning sets
Pinning sets for 12^1_125 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_125 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, 5, 9}
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: [[1,2,3,4],[0,4,4,5],[0,6,7,7],[0,7,7,8],[0,5,1,1],[1,4,8,6],[2,5,9,9],[2,3,3,2],[3,9,9,5],[6,8,8,6]]
PD code (use to draw this loop with SnapPy): [[3,20,4,1],[2,11,3,12],[19,6,20,7],[4,18,5,17],[1,13,2,12],[13,10,14,11],[7,14,8,15],[5,18,6,19],[9,16,10,17],[8,16,9,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,3,-17,-4)(10,7,-11,-8)(19,8,-20,-9)(9,18,-10,-19)(4,11,-5,-12)(12,5,-13,-6)(6,13,-7,-14)(14,1,-15,-2)(2,15,-3,-16)(20,17,-1,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14,-7,10,18)(-2,-16,-4,-12,-6,-14)(-3,16)(-5,12)(-8,19,-10)(-9,-19)(-11,4,-17,20,8)(-13,6)(-15,2)(-18,9,-20)(1,17,3,15)(5,11,7,13)
Loop annotated with half-edges
12^1_125 annotated with half-edges