$12^{2}_{276}$ - Minimal pinning sets
Pinning sets for 12^2_276 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_276 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, 3, 4, 8, 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, 3, 4, 4, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,5,6,6],[0,7,7,8],[1,9,9,5],[1,4,8,2],[2,7,7,2],[3,6,6,3],[3,5,9,9],[4,8,8,4]]
PD code (use to draw this multiloop with SnapPy): [[12,5,1,6],[6,11,7,12],[4,20,5,13],[1,18,2,17],[10,14,11,15],[7,14,8,13],[19,3,20,4],[18,3,19,2],[8,16,9,17],[15,9,16,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,13,-1,-14)(14,1,-15,-2)(10,3,-11,-4)(18,7,-19,-8)(4,9,-5,-10)(6,19,-7,-20)(20,11,-13,-12)(2,15,-3,-16)(16,5,-17,-6)(8,17,-9,-18)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14)(-2,-16,-6,-20,-12,-14)(-3,10,-5,16)(-4,-10)(-7,18,-9,4,-11,20)(-8,-18)(-13,12)(-15,2)(-17,8,-19,6)(1,13,11,3,15)(5,9,17)(7,19)
Multiloop annotated with half-edges
12^2_276 annotated with half-edges