$11^{2}_{48}$ - Minimal pinning sets
Pinning sets for 11^2_48 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_48 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 80
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90697
on average over minimal pinning sets: 2.26667
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, 5, 7, 8}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 2, 3, 4, 7, 8}
6
[2, 2, 2, 2, 3, 3]
2.33
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
1
6
2.5
7
0
0
19
2.74
8
0
0
26
2.94
9
0
0
19
3.09
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
1
78
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],[0,1,5,3],[0,2,5,6],[1,7,7,8],[2,8,8,3],[3,8,7,7],[4,6,6,4],[4,6,5,5]]
PD code (use to draw this multiloop with SnapPy): [[8,18,1,9],[9,7,10,8],[10,17,11,18],[1,11,2,12],[14,6,15,7],[16,2,17,3],[12,4,13,5],[5,13,6,14],[15,4,16,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,8,-10,-1)(1,18,-2,-9)(15,2,-16,-3)(17,4,-18,-5)(12,5,-13,-6)(3,16,-4,-17)(13,10,-14,-11)(6,11,-7,-12)(7,14,-8,-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,-9)(-2,15,-8,9)(-3,-17,-5,12,-7,-15)(-4,17)(-6,-12)(-10,13,5,-18,1)(-11,6,-13)(-14,7,11)(-16,3)(2,18,4,16)(8,14,10)
Multiloop annotated with half-edges
11^2_48 annotated with half-edges