$11^{2}_{49}$ - Minimal pinning sets
Pinning sets for 11^2_49 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_49 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 92
of which optimal: 1
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.91244
on average over minimal pinning sets: 2.38333
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 5, 8}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 2, 4, 5, 7, 8}
6
[2, 2, 2, 2, 3, 3]
2.33
b (minimal)
• {1, 2, 4, 5, 8, 11}
6
[2, 2, 2, 2, 3, 4]
2.50
c (minimal)
• {1, 2, 4, 5, 8, 10}
6
[2, 2, 2, 2, 3, 4]
2.50
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
2.2
6
0
3
6
2.5
7
0
0
24
2.77
8
0
0
30
2.97
9
0
0
20
3.1
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
3
88
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 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],[0,6,7,7],[1,8,8,5],[2,4,6,2],[3,5,8,7],[3,6,8,3],[4,7,6,4]]
PD code (use to draw this multiloop with SnapPy): [[6,18,1,7],[7,5,8,6],[8,17,9,18],[1,13,2,14],[4,10,5,11],[16,9,17,10],[12,15,13,16],[2,15,3,14],[11,3,12,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,6,-8,-1)(15,2,-16,-3)(12,17,-13,-18)(1,18,-2,-7)(4,9,-5,-10)(10,5,-11,-6)(8,11,-9,-12)(16,13,-17,-14)(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,-7)(-2,15,-4,-10,-6,7)(-3,-15)(-5,10)(-8,-12,-18,1)(-9,4,14,-17,12)(-11,8,6)(-13,16,2,18)(-14,3,-16)(5,9,11)(13,17)
Multiloop annotated with half-edges
11^2_49 annotated with half-edges