$11^{2}_{62}$ - Minimal pinning sets
Pinning sets for 11^2_62 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_62 Pinning data
Pinning number of this multiloop: 6
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: 2.78769
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, 6, 10}
6
[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
6
1
0
0
2.0
7
0
0
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 4, 7, 7]
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],[2,8,8,2],[5,8,8,5],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[14,18,1,15],[15,8,16,7],[13,2,14,3],[17,1,18,2],[8,17,9,16],[9,6,10,7],[3,12,4,13],[5,10,6,11],[11,4,12,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(6,3,-7,-4)(4,15,-5,-16)(2,7,-3,-8)(14,9,-1,-10)(17,12,-18,-13)(10,13,-11,-14)(16,5,-17,-6)(11,18,-12,-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)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,-3,6,-17,-13,10)(-2,-8)(-4,-16,-6)(-5,16)(-7,2,-9,14,-11,-15,4)(-10,-14)(-12,17,5,15)(-18,11,13)(1,9)(3,7)(12,18)
Multiloop annotated with half-edges
11^2_62 annotated with half-edges