$12^{2}_{235}$ - Minimal pinning sets
Pinning sets for 12^2_235 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_235 Pinning data
Pinning number of this multiloop: 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, 6, 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 multiloop 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: [[1,1,2,3],[0,4,2,0],[0,1,5,5],[0,6,6,7],[1,7,7,8],[2,8,6,2],[3,5,9,3],[3,9,4,4],[4,9,9,5],[6,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[16,5,1,6],[6,15,7,16],[7,4,8,5],[1,12,2,13],[14,20,15,17],[3,8,4,9],[11,2,12,3],[13,18,14,17],[19,9,20,10],[10,18,11,19]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (4,1,-5,-2)(13,2,-14,-3)(16,5,-1,-6)(17,6,-18,-7)(14,9,-15,-10)(3,12,-4,-13)(8,15,-9,-16)(11,18,-12,-19)(19,10,-20,-11)(7,20,-8,-17)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4,12,18,6)(-2,13,-4)(-3,-13)(-5,16,-9,14,2)(-6,17,-8,-16)(-7,-17)(-10,19,-12,3,-14)(-11,-19)(-15,8,20,10)(-18,11,-20,7)(1,5)(9,15)
Multiloop annotated with half-edges
12^2_235 annotated with half-edges