$11^{2}_{37}$ - Minimal pinning sets
Pinning sets for 11^2_37 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_37 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 152
of which optimal: 5
of which minimal: 5
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.98106
on average over minimal pinning sets: 2.48
on average over optimal pinning sets: 2.48
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 6, 9, 10}
5
[2, 2, 2, 3, 3]
2.40
B (optimal)
• {1, 3, 6, 10, 11}
5
[2, 2, 2, 3, 4]
2.60
C (optimal)
• {1, 2, 4, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
D (optimal)
• {1, 2, 3, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
E (optimal)
• {1, 3, 5, 6, 10}
5
[2, 2, 2, 3, 4]
2.60
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
5
0
0
2.48
6
0
0
23
2.75
7
0
0
44
2.93
8
0
0
45
3.06
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
5
0
147
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,5],[0,5,6,4],[1,3,6,7],[2,8,3,2],[3,8,7,4],[4,6,8,8],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[8,18,1,9],[9,7,10,8],[10,17,11,18],[1,16,2,15],[6,14,7,15],[16,11,17,12],[2,5,3,6],[3,13,4,14],[12,4,13,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(8,3,-1,-4)(16,5,-17,-6)(13,18,-14,-9)(1,10,-2,-11)(4,11,-5,-12)(12,7,-13,-8)(17,14,-18,-15)(6,15,-7,-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,-11,4)(-2,9,-14,17,5,11)(-3,8,-13,-9)(-4,-12,-8)(-5,16,-7,12)(-6,-16)(-10,1,3)(-15,6,-17)(-18,13,7,15)(2,10)(14,18)
Multiloop annotated with half-edges
11^2_37 annotated with half-edges