$12^{2}_{284}$ - Minimal pinning sets
Pinning sets for 12^2_284 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_284 Pinning data
Pinning number of this multiloop: 7
Total number of pinning sets: 32
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: 2.80821
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, 4, 5, 6, 9, 11}
7
[2, 2, 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
7
1
0
0
2.0
8
0
0
5
2.4
9
0
0
10
2.71
10
0
0
10
2.96
11
0
0
5
3.16
12
0
0
1
3.33
Total
1
0
31
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 4, 4, 6, 6, 6]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,4,5,5],[0,6,7,7],[1,8,2,1],[2,9,9,2],[3,9,9,8],[3,8,8,3],[4,7,7,6],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,9,12,10],[19,7,20,8],[1,16,2,15],[8,12,9,13],[6,18,7,19],[16,5,17,4],[2,14,3,15],[13,3,14,4],[17,5,18,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,10,-12,-1)(1,14,-2,-15)(15,2,-16,-3)(17,4,-18,-5)(19,6,-20,-7)(5,20,-6,-11)(9,12,-10,-13)(13,8,-14,-9)(3,16,-4,-17)(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,-15,-3,-17,-5,-11)(-2,15)(-4,17)(-6,19,-8,13,-10,11)(-7,-19)(-9,-13)(-12,9,-14,1)(-16,3)(-18,7,-20,5)(2,14,8,18,4,16)(6,20)(10,12)
Multiloop annotated with half-edges
12^2_284 annotated with half-edges