$11^{2}_{63}$ - Minimal pinning sets
Pinning sets for 11^2_63 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_63 Pinning data
Pinning number of this multiloop: 6
Total number of pinning sets: 32
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: 2.78769
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, 3, 4, 7, 8}
6
[2, 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
6
1
0
0
2.0
7
0
0
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 5, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,6,6],[0,7,8,8],[1,5,5,1],[2,4,4,8],[2,7,7,2],[3,6,6,8],[3,7,5,3]]
PD code (use to draw this multiloop with SnapPy): [[6,18,1,7],[7,5,8,6],[10,17,11,18],[1,13,2,14],[4,8,5,9],[9,3,10,4],[16,11,17,12],[12,15,13,16],[2,15,3,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,1,-15,-2)(12,3,-13,-4)(9,16,-10,-17)(5,18,-6,-7)(7,6,-8,-1)(17,8,-18,-9)(15,10,-16,-11)(4,11,-5,-12)(2,13,-3,-14)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14,-3,12,-5,-7)(-2,-14)(-4,-12)(-6,7)(-8,17,-10,15,1)(-9,-17)(-11,4,-13,2,-15)(-16,9,-18,5,11)(3,13)(6,18,8)(10,16)
Multiloop annotated with half-edges
11^2_63 annotated with half-edges