$12^{2}_{336}$ - Minimal pinning sets
Pinning sets for 12^2_336 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_336 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, 2, 3, 9}
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, 4, 4, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,4,5],[0,5,6,0],[0,6,7,1],[1,7,7,8],[1,8,8,2],[2,9,9,3],[3,9,4,4],[4,9,5,5],[6,8,7,6]]
PD code (use to draw this multiloop with SnapPy): [[5,12,6,1],[4,20,5,13],[11,6,12,7],[1,14,2,13],[17,3,18,4],[19,7,20,8],[10,14,11,15],[2,16,3,17],[18,9,19,8],[15,9,16,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,12,-14,-1)(8,3,-9,-4)(15,4,-16,-5)(5,14,-6,-15)(19,6,-20,-7)(2,9,-3,-10)(11,20,-12,-13)(1,16,-2,-17)(17,10,-18,-11)(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,-17,-11,-13)(-2,-10,17)(-3,8,18,10)(-4,15,-6,19,-8)(-5,-15)(-7,-19)(-9,2,16,4)(-12,13)(-14,5,-16,1)(-18,7,-20,11)(3,9)(6,14,12,20)
Multiloop annotated with half-edges
12^2_336 annotated with half-edges