$12^{2}_{236}$ - Minimal pinning sets
Pinning sets for 12^2_236 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_236 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 128
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: 2.90623
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, 5, 6, 7}
5
[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
5
1
0
0
2.0
6
0
0
7
2.38
7
0
0
21
2.65
8
0
0
35
2.86
9
0
0
35
3.02
10
0
0
21
3.14
11
0
0
7
3.25
12
0
0
1
3.33
Total
1
0
127
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,5],[0,6,6,4],[1,3,7,8],[2,8,6,2],[3,5,7,3],[4,6,9,9],[4,9,9,5],[7,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[14,5,1,6],[6,13,7,14],[7,4,8,5],[1,15,2,20],[12,19,13,20],[3,8,4,9],[15,3,16,2],[16,11,17,12],[18,9,19,10],[10,17,11,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,15,-1,-16)(5,2,-6,-3)(12,3,-13,-4)(1,6,-2,-7)(18,7,-19,-8)(16,9,-17,-10)(4,11,-5,-12)(8,17,-9,-18)(10,19,-11,-20)(20,13,-15,-14)
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,-7,18,-9,16)(-2,5,11,19,7)(-3,12,-5)(-4,-12)(-6,1,15,13,3)(-8,-18)(-10,-20,-14,-16)(-11,4,-13,20)(-15,14)(-17,8,-19,10)(2,6)(9,17)
Multiloop annotated with half-edges
12^2_236 annotated with half-edges