$11^{2}_{7}$ - Minimal pinning sets
Pinning sets for 11^2_7 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_7 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 112
of which optimal: 3
of which minimal: 3
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.91313
on average over minimal pinning sets: 2.26667
on average over optimal pinning sets: 2.26667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 6, 9, 10}
5
[2, 2, 2, 2, 4]
2.40
B (optimal)
• {1, 2, 6, 8, 10}
5
[2, 2, 2, 2, 3]
2.20
C (optimal)
• {1, 2, 5, 6, 10}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
3
0
0
2.27
6
0
0
15
2.6
7
0
0
31
2.83
8
0
0
34
2.99
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
3
0
109
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,5],[0,6,7,7],[0,7,7,6],[0,8,8,1],[1,8,6,1],[2,5,8,3],[2,3,3,2],[4,6,5,4]]
PD code (use to draw this multiloop with SnapPy): [[14,7,1,8],[8,15,9,18],[4,13,5,14],[6,11,7,12],[1,16,2,15],[9,17,10,18],[10,3,11,4],[12,5,13,6],[16,3,17,2]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,14,-8,-1)(9,2,-10,-3)(11,4,-12,-5)(3,8,-4,-9)(1,10,-2,-11)(13,18,-14,-15)(6,15,-7,-16)(16,5,-17,-6)(17,12,-18,-13)
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,-5,16,-7)(-2,9,-4,11)(-3,-9)(-6,-16)(-8,3,-10,1)(-12,17,5)(-13,-15,6,-17)(-14,7,15)(-18,13)(2,10)(4,8,14,18,12)
Multiloop annotated with half-edges
11^2_7 annotated with half-edges