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