$11^{3}_{14}$ - Minimal pinning sets
Pinning sets for 11^3_14 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^3_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)
• {1, 3, 6, 11}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 2, 4, 6, 11}
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],[0,4,5,0],[0,5,5,3],[0,2,6,4],[1,3,6,7],[1,8,2,2],[3,8,7,4],[4,6,8,8],[5,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[8,12,1,9],[9,7,10,8],[11,18,12,13],[1,18,2,17],[6,16,7,17],[10,14,11,13],[2,5,3,6],[3,15,4,16],[14,4,15,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,2,-10,-3)(8,3,-1,-4)(16,5,-17,-6)(6,15,-7,-16)(1,10,-2,-11)(4,11,-5,-12)(12,7,-13,-8)(18,13,-15,-14)(14,17,-9,-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,-11,4)(-2,9,17,5,11)(-3,8,-13,18,-9)(-4,-12,-8)(-5,16,-7,12)(-6,-16)(-10,1,3)(-14,-18)(-15,6,-17,14)(2,10)(7,15,13)
Multiloop annotated with half-edges
11^3_14 annotated with half-edges