$10^{2}_{25}$ - Minimal pinning sets
Pinning sets for 10^2_25 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_25 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, 4, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,4,5,5],[0,5,6,6],[1,7,2,1],[2,7,3,2],[3,7,7,3],[4,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[8,16,1,9],[9,7,10,8],[15,5,16,6],[1,14,2,13],[6,10,7,11],[4,14,5,15],[2,12,3,13],[11,3,12,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,8,-10,-1)(13,2,-14,-3)(15,4,-16,-5)(7,10,-8,-11)(11,6,-12,-7)(1,12,-2,-13)(5,14,-6,-15)(3,16,-4,-9)
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,-9)(-2,13)(-4,15,-6,11,-8,9)(-5,-15)(-7,-11)(-10,7,-12,1)(-14,5,-16,3)(2,12,6,14)(4,16)(8,10)
Multiloop annotated with half-edges
10^2_25 annotated with half-edges