$12^{1}_{183}$ - Minimal pinning sets
Pinning sets for 12^1_183 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_183 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 272
of which optimal: 3
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.0386
on average over minimal pinning sets: 2.46667
on average over optimal pinning sets: 2.4
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 4, 6, 11}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {1, 2, 4, 8, 11}
5
[2, 2, 2, 3, 3]
2.40
C (optimal)
• {1, 2, 4, 6, 11}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {1, 3, 4, 5, 8, 11}
6
[2, 2, 2, 3, 3, 4]
2.67
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
3
0
0
2.4
6
0
1
19
2.68
7
0
0
55
2.89
8
0
0
81
3.04
9
0
0
69
3.15
10
0
0
34
3.24
11
0
0
9
3.29
12
0
0
1
3.33
Total
3
1
268
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,5,6],[0,7,4,4],[0,3,3,8],[1,8,2,1],[2,8,9,7],[3,6,9,9],[4,9,6,5],[6,8,7,7]]
PD code (use to draw this loop with SnapPy): [[20,3,1,4],[4,18,5,17],[19,16,20,17],[9,2,10,3],[1,10,2,11],[18,6,19,5],[12,15,13,16],[13,8,14,9],[11,7,12,6],[7,14,8,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,20,-8,-1)(18,1,-19,-2)(3,16,-4,-17)(4,9,-5,-10)(11,6,-12,-7)(19,8,-20,-9)(5,12,-6,-13)(10,13,-11,-14)(17,14,-18,-15)(15,2,-16,-3)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,14,-11,-7)(-2,15,-18)(-3,-17,-15)(-4,-10,-14,17)(-5,-13,10)(-6,11,13)(-8,19,1)(-9,4,16,2,-19)(-12,5,9,-20,7)(-16,3)(6,12)(8,20)
Loop annotated with half-edges
12^1_183 annotated with half-edges