$10^{1}_{24}$ - Minimal pinning sets
Pinning sets for 10^1_24 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_24 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 32
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: 2.7622
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, 4, 5, 9}
5
[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
5
1
0
0
2.0
6
0
0
5
2.4
7
0
0
10
2.69
8
0
0
10
2.9
9
0
0
5
3.07
10
0
0
1
3.2
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,4,5,5],[0,6,7,7],[1,7,2,1],[2,6,6,2],[3,5,5,7],[3,6,4,3]]
PD code (use to draw this loop with SnapPy): [[5,16,6,1],[15,4,16,5],[6,14,7,13],[1,11,2,10],[3,14,4,15],[7,12,8,13],[11,8,12,9],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(9,6,-10,-7)(16,7,-1,-8)(8,15,-9,-16)(5,10,-6,-11)(11,4,-12,-5)(1,12,-2,-13)(3,14,-4,-15)
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,-13,-3,-15,8)(-2,13)(-4,11,-6,9,15)(-5,-11)(-7,16,-9)(-8,-16)(-10,5,-12,1,7)(-14,3)(2,12,4,14)(6,10)
Loop annotated with half-edges
10^1_24 annotated with half-edges