$12^{1}_{289}$ - Minimal pinning sets
Pinning sets for 12^1_289 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 12^1_289 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, 3, 4, 7, 8, 9}
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, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,5,0],[1,6,7,1],[2,8,8,5],[2,4,9,6],[3,5,9,9],[3,9,8,8],[4,7,7,4],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[9,20,10,1],[19,8,20,9],[10,2,11,1],[7,18,8,19],[2,16,3,15],[11,15,12,14],[6,13,7,14],[17,4,18,5],[16,4,17,3],[12,5,13,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (1,14,-2,-15)(15,2,-16,-3)(10,3,-11,-4)(17,6,-18,-7)(4,11,-5,-12)(12,9,-13,-10)(13,20,-14,-1)(5,16,-6,-17)(7,18,-8,-19)(19,8,-20,-9)
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,-15,-3,10,-13)(-2,15)(-4,-12,-10)(-5,-17,-7,-19,-9,12)(-6,17)(-8,19)(-11,4)(-14,1)(-16,5,11,3)(-18,7)(-20,13,9)(2,14,20,8,18,6,16)
Loop annotated with half-edges
12^1_289 annotated with half-edges