$11^{2}_{52}$ - Minimal pinning sets
Pinning sets for 11^2_52 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_52 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, 3, 5, 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, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,5,6,6],[0,7,4,0],[1,3,7,5],[1,4,2,1],[2,8,8,2],[3,8,8,4],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[6,18,1,7],[7,14,8,15],[9,5,10,6],[17,1,18,2],[13,16,14,17],[8,16,9,15],[4,10,5,11],[2,12,3,13],[11,3,12,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,1,-7,-2)(16,3,-17,-4)(12,5,-13,-6)(2,17,-3,-18)(6,7,-1,-8)(14,9,-15,-10)(10,15,-11,-16)(8,11,-9,-12)(4,13,-5,-14)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,-3,16,-11,8)(-2,-18)(-4,-14,-10,-16)(-5,12,-9,14)(-6,-8,-12)(-7,6,-13,4,-17,2)(-15,10)(1,7)(3,17)(5,13)(9,11,15)
Multiloop annotated with half-edges
11^2_52 annotated with half-edges