$11^{2}_{64}$ - Minimal pinning sets
Pinning sets for 11^2_64 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_64 Pinning data
Pinning number of this multiloop: 7
Total number of pinning sets: 28
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: 2.80455
on average over minimal pinning sets: 2.19048
on average over optimal pinning sets: 2.19048
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 4, 6, 8, 10}
7
[2, 2, 2, 2, 2, 2, 3]
2.14
B (optimal)
• {1, 2, 3, 4, 6, 9, 10}
7
[2, 2, 2, 2, 2, 2, 4]
2.29
C (optimal)
• {1, 2, 3, 4, 5, 6, 10}
7
[2, 2, 2, 2, 2, 2, 3]
2.14
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
7
3
0
0
2.19
8
0
0
9
2.64
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
3
0
25
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 4, 7, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,5,5],[0,6,4,0],[1,3,6,1],[2,7,7,2],[3,8,8,4],[5,8,8,5],[6,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[14,18,1,15],[15,8,16,7],[13,6,14,7],[17,1,18,2],[8,17,9,16],[5,12,6,13],[2,10,3,9],[11,4,12,5],[10,4,11,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,7,-1,-8)(8,1,-9,-2)(10,3,-11,-4)(4,15,-5,-16)(6,13,-7,-14)(2,9,-3,-10)(17,12,-18,-13)(16,5,-17,-6)(11,18,-12,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8)(-2,-10,-4,-16,-6,-14,-8)(-3,10)(-5,16)(-7,14)(-9,2)(-11,-15,4)(-12,17,5,15)(-13,6,-17)(-18,11,3,9,1,7,13)(12,18)
Multiloop annotated with half-edges
11^2_64 annotated with half-edges