$11^{2}_{20}$ - Minimal pinning sets
Pinning sets for 11^2_20 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_20 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 64
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: 2.83846
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, 4, 7, 8, 10}
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
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 3, 3, 7, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,4],[0,5,6,3],[0,2,1,0],[1,7,7,1],[2,8,6,6],[2,5,5,8],[4,8,8,4],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[6,18,1,7],[7,17,8,16],[5,2,6,3],[17,1,18,2],[8,15,9,16],[3,11,4,12],[12,4,13,5],[14,9,15,10],[10,13,11,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(13,4,-14,-5)(2,5,-3,-6)(10,17,-11,-18)(6,7,-1,-8)(18,9,-7,-10)(16,11,-17,-12)(12,15,-13,-16)(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)(-17,17)(-18,18)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8)(-2,-6,-8)(-3,-15,12,-17,10,-7,6)(-4,13,15)(-5,2,-9,18,-11,16,-13)(-10,-18)(-12,-16)(-14,3,5)(1,7,9)(4,14)(11,17)
Multiloop annotated with half-edges
11^2_20 annotated with half-edges