$11^{2}_{26}$ - Minimal pinning sets
Pinning sets for 11^2_26 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_26 Pinning data
Pinning number of this multiloop: 4
Total number of pinning sets: 128
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: 2.89692
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, 4, 8}
4
[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
4
1
0
0
2.0
5
0
0
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,6,7],[0,8,1,0],[1,8,5,5],[1,4,4,6],[2,5,7,2],[2,6,8,8],[3,7,7,4]]
PD code (use to draw this multiloop with SnapPy): [[12,18,1,13],[13,17,14,16],[11,4,12,5],[17,1,18,2],[14,8,15,9],[9,15,10,16],[5,10,6,11],[6,3,7,4],[2,7,3,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (4,1,-5,-2)(9,2,-10,-3)(12,5,-1,-6)(13,6,-14,-7)(3,8,-4,-9)(16,11,-17,-12)(7,14,-8,-15)(15,18,-16,-13)(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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4,8,14,6)(-2,9,-4)(-3,-9)(-5,12,-17,10,2)(-6,13,-16,-12)(-7,-15,-13)(-8,3,-10,-18,15)(-11,16,18)(-14,7)(1,5)(11,17)
Multiloop annotated with half-edges
11^2_26 annotated with half-edges