$10^{2}_{23}$ - Minimal pinning sets
Pinning sets for 10^2_23 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_23 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, 3, 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 multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,6,6,3],[0,2,4,0],[1,3,5,1],[1,4,7,7],[2,7,7,2],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[12,16,1,13],[13,7,14,8],[11,2,12,3],[15,1,16,2],[6,14,7,15],[8,6,9,5],[3,10,4,11],[9,4,10,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,3,-1,-4)(13,2,-14,-3)(10,5,-11,-6)(15,8,-16,-9)(6,9,-7,-10)(4,11,-5,-12)(7,16,-8,-13)(1,14,-2,-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,-15,-9,6,-11,4)(-2,13,-8,15)(-3,12,-5,10,-7,-13)(-4,-12)(-6,-10)(-14,1,3)(-16,7,9)(2,14)(5,11)(8,16)
Multiloop annotated with half-edges
10^2_23 annotated with half-edges