$11^{2}_{1}$ - Minimal pinning sets
Pinning sets for 11^2_1 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_1 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 64
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: 2.83846
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, 8}
5
[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
5
1
0
0
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,5],[0,6,6,3],[0,2,1,0],[1,6,7,7],[1,8,8,6],[2,5,4,2],[4,8,8,4],[5,7,7,5]]
PD code (use to draw this multiloop with SnapPy): [[10,18,1,11],[11,17,12,16],[9,2,10,3],[17,1,18,2],[12,4,13,5],[7,15,8,16],[3,8,4,9],[13,6,14,5],[14,6,15,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,10,-8,-1)(11,2,-12,-3)(3,12,-4,-13)(13,4,-14,-5)(1,6,-2,-7)(16,9,-17,-10)(5,14,-6,-15)(15,18,-16,-11)(8,17,-9,-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,-7)(-2,11,-16,-10,7)(-3,-13,-5,-15,-11)(-4,13)(-6,1,-8,-18,15)(-9,16,18)(-12,3)(-14,5)(-17,8,10)(2,6,14,4,12)(9,17)
Multiloop annotated with half-edges
11^2_1 annotated with half-edges