$12^{2}_{279}$ - Minimal pinning sets
Pinning sets for 12^2_279 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_279 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 64
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: 2.85421
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}
6
[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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,5],[0,5,5,0],[0,6,7,7],[1,8,9,1],[1,9,2,2],[3,9,9,8],[3,8,8,3],[4,7,7,6],[4,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[10,20,1,11],[11,7,12,8],[19,9,20,10],[1,16,2,15],[6,12,7,13],[8,18,9,19],[16,5,17,4],[2,14,3,15],[13,3,14,4],[17,5,18,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (20,1,-11,-2)(2,13,-3,-14)(14,3,-15,-4)(18,5,-19,-6)(16,7,-17,-8)(6,15,-7,-16)(8,17,-9,-18)(4,19,-5,-20)(10,11,-1,-12)(12,9,-13,-10)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,20,-5,18,-9,12)(-2,-14,-4,-20)(-3,14)(-6,-16,-8,-18)(-7,16)(-10,-12)(-11,10,-13,2)(-15,6,-19,4)(-17,8)(1,11)(3,13,9,17,7,15)(5,19)
Multiloop annotated with half-edges
12^2_279 annotated with half-edges