$11^{3}_{3}$ - Minimal pinning sets
Pinning sets for 11^3_3 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^3_3 Pinning data
Pinning number of this multiloop: 3
Total number of pinning sets: 256
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: 2.96519
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)
• {2, 4, 8}
3
[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
3
1
0
0
2.0
4
0
0
8
2.44
5
0
0
28
2.7
6
0
0
56
2.88
7
0
0
70
3.0
8
0
0
56
3.09
9
0
0
28
3.17
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
0
255
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 3, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,3,3],[0,2,2,6],[0,5,1,1],[1,4,7,8],[2,8,7,3],[5,6,8,8],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[3,6,4,1],[2,12,3,7],[5,18,6,13],[4,18,5,17],[1,8,2,7],[8,11,9,12],[13,16,14,17],[14,10,15,11],[9,15,10,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (1,4,-2,-5)(16,11,-17,-12)(9,12,-10,-7)(6,7,-1,-8)(8,5,-9,-6)(10,17,-11,-18)(15,18,-16,-13)(13,2,-14,-3)(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,-5,8)(-2,13,-16,-12,9,5)(-3,-15,-13)(-4,1,7,-10,-18,15)(-6,-8)(-7,6,-9)(-11,16,18)(-14,3)(-17,10,12)(2,4,14)(11,17)
Multiloop annotated with half-edges
11^3_3 annotated with half-edges