$12^{1}_{285}$ - Minimal pinning sets
Pinning sets for 12^1_285 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_285 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 464
of which optimal: 1
of which minimal: 6
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.11482
on average over minimal pinning sets: 2.68333
on average over optimal pinning sets: 2.5
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {2, 6, 7, 11}
4
[2, 2, 3, 3]
2.50
a (minimal)
• {2, 4, 5, 7, 11}
5
[2, 2, 3, 3, 4]
2.80
b (minimal)
• {1, 2, 5, 7, 11}
5
[2, 2, 3, 3, 3]
2.60
c (minimal)
• {2, 5, 7, 8, 11}
5
[2, 2, 3, 3, 4]
2.80
d (minimal)
• {1, 2, 5, 10, 11}
5
[2, 2, 3, 3, 3]
2.60
e (minimal)
• {2, 5, 8, 10, 11}
5
[2, 2, 3, 3, 4]
2.80
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
2.5
5
0
5
8
2.74
6
0
0
54
2.92
7
0
0
112
3.05
8
0
0
134
3.15
9
0
0
97
3.22
10
0
0
42
3.27
11
0
0
10
3.31
12
0
0
1
3.33
Total
1
5
458
Other information about this loop Properties
Region degree sequence: [2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,5],[0,5,6,0],[0,6,7,8],[1,8,9,1],[1,9,6,2],[2,5,7,3],[3,6,9,8],[3,7,9,4],[4,8,7,5]]
PD code (use to draw this loop with SnapPy): [[20,13,1,14],[14,5,15,6],[12,19,13,20],[1,8,2,9],[4,15,5,16],[6,11,7,12],[7,18,8,19],[2,18,3,17],[9,17,10,16],[10,3,11,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,20,-10,-1)(16,3,-17,-4)(1,6,-2,-7)(15,8,-16,-9)(19,10,-20,-11)(11,4,-12,-5)(12,17,-13,-18)(2,13,-3,-14)(7,14,-8,-15)(5,18,-6,-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,-7,-15,-9)(-2,-14,7)(-3,16,8,14)(-4,11,-20,9,-16)(-5,-19,-11)(-6,1,-10,19)(-8,15)(-12,-18,5)(-13,2,6,18)(-17,12,4)(3,13,17)(10,20)
Loop annotated with half-edges
12^1_285 annotated with half-edges