$10^{2}_{1}$ - Minimal pinning sets
Pinning sets for 10^2_1 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^2_1 Pinning data
Pinning number of this multiloop: 8
Total number of pinning sets: 4
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: 2.63333
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, 4, 5, 6, 7, 9}
8
[2, 2, 2, 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
8
1
0
0
2.0
9
0
0
2
2.67
10
0
0
1
3.2
Total
1
0
3
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 2, 8, 8]
Minimal region degree: 2
Is multisimple: Yes
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,5,1],[2,6,6,2],[3,7,7,3],[4,7,7,4],[5,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[8,16,1,9],[9,7,10,8],[15,1,16,2],[6,10,7,11],[2,14,3,15],[11,5,12,6],[13,3,14,4],[4,12,5,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,8,-10,-1)(15,2,-16,-3)(13,4,-14,-5)(11,6,-12,-7)(1,16,-2,-9)(7,10,-8,-11)(5,12,-6,-13)(3,14,-4,-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,-9)(-2,15,-4,13,-6,11,-8,9)(-3,-15)(-5,-13)(-7,-11)(-10,7,-12,5,-14,3,-16,1)(2,16)(4,14)(6,12)(8,10)
Multiloop annotated with half-edges
10^2_1 annotated with half-edges