$11^{2}_{75}$ - Minimal pinning sets
Pinning sets for 11^2_75
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_75
Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 208
of which optimal: 2
of which minimal: 3
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.98127
on average over minimal pinning sets: 2.43333
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
•
{1, 2, 3, 9}
4
[2, 2, 2, 3]
2.25
B (optimal)
•
{1, 2, 3, 4}
4
[2, 2, 2, 3]
2.25
a (minimal)
•
{1, 2, 3, 7, 10}
5
[2, 2, 2, 4, 4]
2.80
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
2
0
0
2.25
5
0
1
13
2.6
6
0
0
40
2.83
7
0
0
61
2.98
8
0
0
54
3.09
9
0
0
28
3.17
10
0
0
8
3.23
11
0
0
1
3.27
Total
2
1
205
Other information about this multiloop
Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,4,5],[0,6,6,0],[0,7,8,1],[1,8,8,5],[1,4,7,6],[2,5,7,2],[3,6,5,8],[3,7,4,4]]
PD code (use to draw this multiloop with SnapPy): [[5,14,6,1],[4,18,5,15],[13,6,14,7],[1,16,2,15],[10,3,11,4],[11,17,12,18],[7,12,8,13],[16,8,17,9],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(11,4,-12,-5)(17,6,-18,-7)(14,7,-1,-8)(5,10,-6,-11)(3,12,-4,-13)(9,18,-10,-15)(2,15,-3,-16)(16,13,-17,-14)
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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8)(-2,-16,-14,-8)(-3,-13,16)(-4,11,-6,17,13)(-5,-11)(-7,14,-17)(-9,-15,2)(-10,5,-12,3,15)(-18,9,1,7)(4,12)(6,10,18)
Multiloop annotated with half-edges
11^2_75 annotated with half-edges