$10^{1}_{14}$ - Minimal pinning sets
Pinning sets for 10^1_14 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_14 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.89501
on average over minimal pinning sets: 2.25
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 9}
4
[2, 2, 2, 3]
2.25
B (optimal)
• {1, 2, 4, 7}
4
[2, 2, 2, 3]
2.25
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
2
0
0
2.25
5
0
0
11
2.58
6
0
0
25
2.8
7
0
0
30
2.95
8
0
0
20
3.06
9
0
0
7
3.14
10
0
0
1
3.2
Total
2
0
94
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,6,6,7],[0,7,7,4],[0,3,7,5],[1,4,6,1],[1,5,2,2],[2,4,3,3]]
PD code (use to draw this loop with SnapPy): [[7,16,8,1],[13,6,14,7],[15,10,16,11],[8,3,9,4],[1,4,2,5],[5,12,6,13],[14,12,15,11],[2,9,3,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(15,2,-16,-3)(11,4,-12,-5)(16,7,-1,-8)(13,8,-14,-9)(9,12,-10,-13)(3,10,-4,-11)(5,14,-6,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6,14,8)(-2,15,-6)(-3,-11,-5,-15)(-4,11)(-7,16,2)(-8,13,-10,3,-16)(-9,-13)(-12,9,-14,5)(1,7)(4,10,12)
Loop annotated with half-edges
10^1_14 annotated with half-edges