$12^{1}_{309}$ - Minimal pinning sets
Pinning sets for 12^1_309 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_309 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 64
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: 2.85421
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, 4, 5, 6, 9, 11}
6
[2, 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
6
1
0
0
2.0
7
0
0
6
2.38
8
0
0
15
2.67
9
0
0
20
2.89
10
0
0
15
3.07
11
0
0
6
3.21
12
0
0
1
3.33
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,3],[0,2,7,7],[1,5,5,1],[2,4,4,8],[2,8,8,9],[3,9,9,3],[5,9,6,6],[6,8,7,7]]
PD code (use to draw this loop with SnapPy): [[13,20,14,1],[19,12,20,13],[14,10,15,9],[1,9,2,8],[11,18,12,19],[10,18,11,17],[15,5,16,4],[2,7,3,8],[16,5,17,6],[6,3,7,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (3,20,-4,-1)(1,12,-2,-13)(13,2,-14,-3)(19,4,-20,-5)(5,18,-6,-19)(6,11,-7,-12)(16,9,-17,-10)(14,7,-15,-8)(8,15,-9,-16)(10,17,-11,-18)
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,-13,-3)(-2,13)(-4,19,-6,-12,1)(-5,-19)(-7,14,2,12)(-8,-16,-10,-18,5,-20,3,-14)(-9,16)(-11,6,18)(-15,8)(-17,10)(4,20)(7,11,17,9,15)
Loop annotated with half-edges
12^1_309 annotated with half-edges