$12^{2}_{115}$ - Minimal pinning sets
Pinning sets for 12^2_115 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_115 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, 5, 7, 11}
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, 3, 3, 3, 8, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,5,0],[0,4,1,1],[1,3,6,6],[2,7,7,2],[4,8,9,4],[5,9,8,5],[6,7,9,9],[6,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[3,12,4,1],[2,20,3,13],[11,4,12,5],[1,14,2,13],[14,19,15,20],[5,10,6,11],[18,15,19,16],[9,6,10,7],[16,9,17,8],[17,7,18,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(7,4,-8,-5)(18,5,-19,-6)(6,17,-7,-18)(3,8,-4,-9)(1,10,-2,-11)(19,16,-20,-17)(15,20,-16,-13)(12,13,-1,-14)(14,11,-15,-12)
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,-11,14)(-2,9,-4,7,17,-20,15,11)(-3,-9)(-5,18,-7)(-6,-18)(-8,3,-10,1,13,-16,19,5)(-12,-14)(-13,12,-15)(-17,6,-19)(2,10)(4,8)(16,20)
Multiloop annotated with half-edges
12^2_115 annotated with half-edges