$11^{2}_{41}$ - Minimal pinning sets
Pinning sets for 11^2_41 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_41 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, 6, 10}
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, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,5],[0,5,6,7],[1,7,7,8],[2,8,3,2],[3,8,8,7],[3,6,4,4],[4,6,6,5]]
PD code (use to draw this multiloop with SnapPy): [[7,14,8,1],[13,6,14,7],[8,6,9,5],[1,10,2,11],[12,18,13,15],[9,4,10,5],[2,17,3,16],[11,16,12,15],[3,17,4,18]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,2,-8,-3)(3,6,-4,-7)(11,4,-12,-5)(13,8,-14,-9)(5,12,-6,-13)(10,17,-11,-18)(18,9,-15,-10)(15,14,-16,-1)(1,16,-2,-17)
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,-17,10,-15)(-2,7,-4,11,17)(-3,-7)(-5,-13,-9,18,-11)(-6,3,-8,13)(-10,-18)(-12,5)(-14,15,9)(-16,1)(2,16,14,8)(4,6,12)
Multiloop annotated with half-edges
11^2_41 annotated with half-edges