$11^{2}_{2}$ - Minimal pinning sets
Pinning sets for 11^2_2 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_2 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, 4, 5, 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, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,5,6,3],[0,2,4,0],[1,3,7,1],[1,8,8,2],[2,8,7,7],[4,6,6,8],[5,7,6,5]]
PD code (use to draw this multiloop with SnapPy): [[14,18,1,15],[15,10,16,9],[13,2,14,3],[17,1,18,2],[10,17,11,16],[8,3,9,4],[5,12,6,13],[11,6,12,7],[4,7,5,8]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,2,-8,-3)(14,3,-1,-4)(5,18,-6,-15)(1,8,-2,-9)(16,11,-17,-12)(9,12,-10,-13)(4,13,-5,-14)(15,6,-16,-7)(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,-9,-13,4)(-2,7,-16,-12,9)(-3,14,-5,-15,-7)(-4,-14)(-6,15)(-8,1,3)(-10,-18,5,13)(-11,16,6,18)(-17,10,12)(2,8)(11,17)
Multiloop annotated with half-edges
11^2_2 annotated with half-edges