$10^{1}_{4}$ - Minimal pinning sets
Pinning sets for 10^1_4 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_4 Pinning data
Pinning number of this loop: 4
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: 2.8189
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, 5, 7}
4
[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
4
1
0
0
2.0
5
0
0
6
2.4
6
0
0
15
2.67
7
0
0
20
2.86
8
0
0
15
3.0
9
0
0
6
3.11
10
0
0
1
3.2
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,6,3],[0,2,1,0],[1,6,7,7],[1,7,7,6],[2,5,4,2],[4,5,5,4]]
PD code (use to draw this loop with SnapPy): [[16,9,1,10],[10,8,11,7],[15,2,16,3],[8,1,9,2],[11,4,12,5],[13,6,14,7],[3,14,4,15],[12,6,13,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,16,-14,-1)(9,2,-10,-3)(3,10,-4,-11)(11,4,-12,-5)(5,8,-6,-9)(14,7,-15,-8)(1,12,-2,-13)(6,15,-7,-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,-13)(-2,9,-6,-16,13)(-3,-11,-5,-9)(-4,11)(-7,14,16)(-8,5,-12,1,-14)(-10,3)(-15,6,8)(2,12,4,10)(7,15)
Loop annotated with half-edges
10^1_4 annotated with half-edges