$11^{2}_{59}$ - Minimal pinning sets
Pinning sets for 11^2_59 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_59 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, 4, 6, 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 multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,3,3],[0,2,2,6],[1,7,8,1],[2,8,8,6],[3,5,7,7],[4,6,6,8],[4,7,5,5]]
PD code (use to draw this multiloop with SnapPy): [[14,3,1,4],[4,13,5,14],[2,9,3,10],[1,9,2,8],[12,5,13,6],[10,15,11,18],[7,17,8,18],[6,17,7,16],[11,15,12,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (12,1,-13,-2)(10,3,-11,-4)(6,13,-7,-14)(14,7,-1,-8)(2,11,-3,-12)(5,16,-6,-17)(17,8,-18,-9)(9,18,-10,-15)(15,4,-16,-5)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-3,10,18,8)(-2,-12)(-4,15,-10)(-5,-17,-9,-15)(-6,-14,-8,17)(-7,14)(-11,2,-13,6,16,4)(-16,5)(-18,9)(1,7,13)(3,11)
Multiloop annotated with half-edges
11^2_59 annotated with half-edges