$12^{2}_{163}$ - Minimal pinning sets
Pinning sets for 12^2_163 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_163 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, 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, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,6,6],[0,6,6,7],[0,7,8,8],[1,9,7,1],[2,3,3,2],[3,5,9,4],[4,9,9,4],[5,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[8,20,1,9],[9,16,10,17],[17,7,18,8],[19,5,20,6],[1,14,2,13],[15,10,16,11],[6,18,7,19],[4,14,5,15],[2,12,3,13],[11,3,12,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,8,-10,-1)(17,2,-18,-3)(15,4,-16,-5)(7,10,-8,-11)(11,6,-12,-7)(1,12,-2,-13)(19,14,-20,-15)(3,16,-4,-17)(5,18,-6,-19)(13,20,-14,-9)
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,-13,-9)(-2,17,-4,15,-20,13)(-3,-17)(-5,-19,-15)(-6,11,-8,9,-14,19)(-7,-11)(-10,7,-12,1)(-16,3,-18,5)(2,12,6,18)(4,16)(8,10)(14,20)
Multiloop annotated with half-edges
12^2_163 annotated with half-edges