$11^{1}_{86}$ - Minimal pinning sets
Pinning sets for 11^1_86 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_86 Pinning data
Pinning number of this loop: 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, 5, 8, 10}
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 loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,4,2],[0,1,5,0],[0,6,7,7],[1,8,5,1],[2,4,6,6],[3,5,5,8],[3,8,8,3],[4,7,7,6]]
PD code (use to draw this loop with SnapPy): [[18,9,1,10],[10,7,11,8],[8,17,9,18],[1,15,2,14],[6,11,7,12],[16,5,17,6],[15,5,16,4],[2,13,3,14],[12,3,13,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,18,-10,-1)(1,12,-2,-13)(13,2,-14,-3)(7,4,-8,-5)(15,6,-16,-7)(3,8,-4,-9)(17,10,-18,-11)(11,16,-12,-17)(5,14,-6,-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,-13,-3,-9)(-2,13)(-4,7,-16,11,-18,9)(-5,-15,-7)(-6,15)(-8,3,-14,5)(-10,17,-12,1)(-11,-17)(2,12,16,6,14)(4,8)(10,18)
Loop annotated with half-edges
11^1_86 annotated with half-edges