$12^{2}_{203}$ - Minimal pinning sets
Pinning sets for 12^2_203 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^2_203 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 384
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.03466
on average over minimal pinning sets: 2.25
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 6, 11}
4
[2, 2, 2, 3]
2.25
B (optimal)
• {1, 3, 4, 11}
4
[2, 2, 2, 3]
2.25
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
2
0
0
2.25
5
0
0
15
2.59
6
0
0
49
2.81
7
0
0
91
2.97
8
0
0
105
3.08
9
0
0
77
3.17
10
0
0
35
3.24
11
0
0
9
3.29
12
0
0
1
3.33
Total
2
0
382
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,3],[0,2,6,4],[1,3,7,8],[2,8,9,6],[3,5,7,7],[4,6,6,9],[4,9,9,5],[5,8,8,7]]
PD code (use to draw this multiloop with SnapPy): [[6,20,1,7],[7,5,8,6],[8,19,9,20],[1,9,2,10],[10,4,11,5],[18,15,19,16],[2,15,3,14],[3,13,4,14],[11,17,12,16],[12,17,13,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,1,-19,-2)(15,2,-16,-3)(4,17,-5,-18)(6,7,-1,-8)(8,5,-9,-6)(12,9,-13,-10)(10,19,-11,-20)(20,11,-7,-12)(16,13,-17,-14)(3,14,-4,-15)
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,-5,8)(-2,15,-4,-18)(-3,-15)(-6,-8)(-7,6,-9,12)(-10,-20,-12)(-11,20)(-13,16,2,-19,10)(-14,3,-16)(-17,4,14)(1,7,11,19)(5,17,13,9)
Multiloop annotated with half-edges
12^2_203 annotated with half-edges