$12^{2}_{146}$ - Minimal pinning sets
Pinning sets for 12^2_146 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_146 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 256
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: 2.96564
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, 3, 4, 11}
4
[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
4
1
0
0
2.0
5
0
0
8
2.4
6
0
0
28
2.67
7
0
0
56
2.86
8
0
0
70
3.0
9
0
0
56
3.11
10
0
0
28
3.2
11
0
0
8
3.27
12
0
0
1
3.33
Total
1
0
255
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,7,8],[0,8,1,0],[1,7,6,5],[1,4,9,9],[2,9,9,4],[2,4,8,8],[2,7,7,3],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[12,20,1,13],[13,19,14,18],[8,11,9,12],[19,1,20,2],[14,4,15,5],[5,17,6,18],[7,15,8,16],[10,3,11,4],[9,3,10,2],[16,6,17,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,12,-8,-1)(18,1,-19,-2)(20,3,-13,-4)(5,8,-6,-9)(15,10,-16,-11)(11,6,-12,-7)(2,13,-3,-14)(14,17,-15,-18)(9,16,-10,-17)(4,19,-5,-20)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,-15,-11,-7)(-2,-14,-18)(-3,20,-5,-9,-17,14)(-4,-20)(-6,11,-16,9)(-8,5,19,1)(-10,15,17)(-12,7)(-13,2,-19,4)(3,13)(6,8,12)(10,16)
Multiloop annotated with half-edges
12^2_146 annotated with half-edges