$11^{2}_{14}$ - Minimal pinning sets
Pinning sets for 11^2_14 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_14 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 160
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: 2.97092
on average over minimal pinning sets: 2.325
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {3, 4, 6, 10}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 2, 4, 6, 10}
5
[2, 2, 2, 3, 3]
2.40
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
4
1
0
0
2.25
5
0
1
7
2.55
6
0
0
26
2.77
7
0
0
45
2.93
8
0
0
45
3.06
9
0
0
26
3.15
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
1
158
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,4,0],[0,4,4,5],[0,5,6,1],[1,7,2,2],[2,8,6,3],[3,5,8,7],[4,6,8,8],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[14,18,1,15],[15,13,16,14],[17,7,18,8],[1,12,2,13],[16,9,17,8],[11,6,12,7],[2,6,3,5],[9,5,10,4],[10,3,11,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,5,-1,-6)(1,12,-2,-13)(7,2,-8,-3)(16,3,-17,-4)(4,15,-5,-16)(11,8,-12,-9)(18,9,-15,-10)(6,13,-7,-14)(10,17,-11,-18)
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,-13,6)(-2,7,13)(-3,16,-5,14,-7)(-4,-16)(-6,-14)(-8,11,17,3)(-9,18,-11)(-10,-18)(-12,1,5,15,9)(-15,4,-17,10)(2,12,8)
Multiloop annotated with half-edges
11^2_14 annotated with half-edges