$12^{2}_{246}$ - Minimal pinning sets
Pinning sets for 12^2_246 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_246 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, 3, 4, 6, 9}
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, 3, 4, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,2],[0,1,6,6],[0,7,7,0],[1,8,8,5],[1,4,9,9],[2,9,7,2],[3,6,8,3],[4,7,9,4],[5,8,6,5]]
PD code (use to draw this multiloop with SnapPy): [[11,16,12,1],[5,10,6,11],[6,15,7,16],[12,2,13,1],[4,20,5,17],[9,19,10,20],[14,7,15,8],[2,14,3,13],[17,3,18,4],[18,8,19,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(20,3,-17,-4)(16,5,-1,-6)(8,13,-9,-14)(1,10,-2,-11)(6,11,-7,-12)(12,7,-13,-8)(19,14,-20,-15)(4,17,-5,-18)(15,18,-16,-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,-11,6)(-2,9,13,7,11)(-3,20,14,-9)(-4,-18,15,-20)(-5,16,18)(-6,-12,-8,-14,19,-16)(-7,12)(-10,1,5,17,3)(-13,8)(-15,-19)(-17,4)(2,10)
Multiloop annotated with half-edges
12^2_246 annotated with half-edges