$12^{2}_{217}$ - Minimal pinning sets
Pinning sets for 12^2_217 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_217 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 192
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.96906
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 5, 9, 11}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 5, 9, 11}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.2
6
0
0
13
2.54
7
0
0
36
2.78
8
0
0
55
2.95
9
0
0
50
3.09
10
0
0
27
3.19
11
0
0
8
3.27
12
0
0
1
3.33
Total
2
0
190
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,5,6],[0,6,7,4],[0,3,8,8],[1,8,2,1],[2,9,9,3],[3,9,9,8],[4,7,5,4],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[5,14,6,1],[4,11,5,12],[13,10,14,11],[6,15,7,20],[1,20,2,19],[12,3,13,4],[9,15,10,16],[7,17,8,18],[2,18,3,19],[16,8,17,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (10,1,-11,-2)(19,6,-20,-7)(11,8,-12,-9)(2,9,-3,-10)(3,12,-4,-13)(5,20,-6,-15)(14,15,-1,-16)(16,13,-17,-14)(17,4,-18,-5)(7,18,-8,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10,-3,-13,16)(-2,-10)(-4,17,13)(-5,-15,14,-17)(-6,19,-8,11,1,15)(-7,-19)(-9,2,-11)(-12,3,9)(-14,-16)(-18,7,-20,5)(4,12,8,18)(6,20)
Multiloop annotated with half-edges
12^2_217 annotated with half-edges