$10^{1}_{2}$ - Minimal pinning sets
Pinning sets for 10^1_2 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_2 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 16
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: 2.71339
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, 2, 3, 4, 7, 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
4
2.43
8
0
0
6
2.75
9
0
0
4
3.0
10
0
0
1
3.2
Total
1
0
15
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,6,6,4],[0,7,7,0],[1,7,7,2],[1,6,6,1],[2,5,5,2],[3,4,4,3]]
PD code (use to draw this loop with SnapPy): [[16,11,1,12],[12,8,13,7],[15,4,16,5],[10,1,11,2],[8,3,9,4],[13,6,14,7],[5,14,6,15],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(13,2,-14,-3)(11,4,-12,-5)(5,10,-6,-11)(16,7,-1,-8)(14,9,-15,-10)(3,12,-4,-13)(8,15,-9,-16)
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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,10,-15,8)(-2,13,-4,11,-6)(-3,-13)(-5,-11)(-7,16,-9,14,2)(-8,-16)(-10,5,-12,3,-14)(1,7)(4,12)(9,15)
Loop annotated with half-edges
10^1_2 annotated with half-edges