$11^{2}_{51}$ - Minimal pinning sets
Pinning sets for 11^2_51 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_51 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, 4, 7, 8}
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, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,5,3],[0,2,6,7],[1,7,8,1],[2,8,8,2],[3,8,7,7],[3,6,6,4],[4,6,5,5]]
PD code (use to draw this multiloop with SnapPy): [[10,18,1,11],[11,9,12,10],[17,5,18,6],[1,5,2,4],[8,12,9,13],[6,16,7,17],[2,15,3,14],[3,13,4,14],[15,7,16,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (2,9,-3,-10)(14,3,-15,-4)(12,5,-13,-6)(16,7,-17,-8)(6,17,-7,-18)(1,18,-2,-11)(11,10,-12,-1)(4,13,-5,-14)(8,15,-9,-16)
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,-11)(-2,-10,11)(-3,14,-5,12,10)(-4,-14)(-6,-18,1,-12)(-7,16,-9,2,18)(-8,-16)(-13,4,-15,8,-17,6)(3,9,15)(5,13)(7,17)
Multiloop annotated with half-edges
11^2_51 annotated with half-edges