$12^{2}_{131}$ - Minimal pinning sets
Pinning sets for 12^2_131 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_131 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, 3, 5, 11}
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, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,7],[0,7,8,9],[1,9,9,1],[2,9,6,6],[2,5,5,8],[2,8,8,3],[3,7,7,6],[3,5,4,4]]
PD code (use to draw this multiloop with SnapPy): [[8,20,1,9],[9,7,10,8],[19,16,20,17],[1,4,2,5],[6,10,7,11],[17,12,18,13],[13,18,14,19],[3,15,4,16],[2,15,3,14],[5,12,6,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,8,-6,-1)(20,3,-9,-4)(2,9,-3,-10)(10,1,-11,-2)(16,11,-17,-12)(13,6,-14,-7)(7,14,-8,-15)(18,15,-19,-16)(12,17,-13,-18)(4,19,-5,-20)
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,-3,20,-5)(-2,-10)(-4,-20)(-6,13,17,11,1)(-7,-15,18,-13)(-8,5,19,15)(-9,2,-11,16,-19,4)(-12,-18,-16)(-14,7)(-17,12)(3,9)(6,8,14)
Multiloop annotated with half-edges
12^2_131 annotated with half-edges