$12^{3}_{38}$ - Minimal pinning sets
Pinning sets for 12^3_38
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^3_38
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, 5, 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, 3, 4, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,4],[0,5,6,6],[0,6,1,0],[1,7,8,1],[2,8,8,9],[2,9,3,2],[4,9,9,8],[4,7,5,5],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[4,16,1,5],[5,15,6,14],[9,3,10,4],[15,1,16,2],[6,13,7,14],[8,20,9,17],[2,10,3,11],[12,18,13,19],[7,18,8,17],[19,11,20,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,1,-5,-2)(10,3,-11,-4)(4,5,-1,-6)(17,6,-18,-7)(13,8,-14,-9)(9,12,-10,-13)(2,11,-3,-12)(15,18,-16,-19)(19,14,-20,-15)(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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,16,18,6)(-2,-12,9,-14,19,-16)(-3,10,12)(-4,-6,17,-8,13,-10)(-5,4,-11,2)(-7,-17)(-9,-13)(-15,-19)(-18,15,-20,7)(1,5)(3,11)(8,20,14)
Multiloop annotated with half-edges
12^3_38 annotated with half-edges