$11^{2}_{56}$ - Minimal pinning sets
Pinning sets for 11^2_56 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_56 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, 2, 3, 5, 6}
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, 4, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,5,0],[0,6,6,3],[0,2,7,4],[1,3,8,8],[1,7,6,6],[2,5,5,2],[3,5,8,8],[4,7,7,4]]
PD code (use to draw this multiloop with SnapPy): [[6,18,1,7],[7,5,8,6],[10,17,11,18],[1,11,2,12],[12,4,13,5],[8,15,9,16],[16,9,17,10],[2,15,3,14],[3,13,4,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,1,-7,-2)(13,2,-14,-3)(10,15,-11,-16)(4,17,-5,-18)(6,7,-1,-8)(8,5,-9,-6)(14,9,-15,-10)(16,11,-17,-12)(3,12,-4,-13)
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,-5,8)(-2,13,-4,-18)(-3,-13)(-6,-8)(-7,6,-9,14,2)(-10,-16,-12,3,-14)(-11,16)(-15,10)(-17,4,12)(1,7)(5,17,11,15,9)
Multiloop annotated with half-edges
11^2_56 annotated with half-edges