$11^{2}_{19}$ - Minimal pinning sets
Pinning sets for 11^2_19 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_19 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 112
of which optimal: 3
of which minimal: 3
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.91313
on average over minimal pinning sets: 2.26667
on average over optimal pinning sets: 2.26667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 3, 5, 8, 10}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 3, 5, 8, 11}
5
[2, 2, 2, 2, 4]
2.40
C (optimal)
• {1, 3, 5, 7, 8}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
3
0
0
2.27
6
0
0
15
2.6
7
0
0
31
2.83
8
0
0
34
2.99
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
3
0
109
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 4, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,4,1,1],[1,3,7,8],[2,8,8,6],[2,5,7,7],[4,6,6,8],[4,7,5,5]]
PD code (use to draw this multiloop with SnapPy): [[3,14,4,1],[9,2,10,3],[13,4,14,5],[1,8,2,9],[10,8,11,7],[5,15,6,18],[12,17,13,18],[11,17,12,16],[6,15,7,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,14,-8,-1)(11,2,-12,-3)(5,8,-6,-9)(13,6,-14,-7)(1,12,-2,-13)(10,17,-11,-18)(18,3,-15,-4)(4,15,-5,-16)(16,9,-17,-10)
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,-13,-7)(-2,11,17,9,-6,13)(-3,18,-11)(-4,-16,-10,-18)(-5,-9,16)(-8,5,15,3,-12,1)(-14,7)(-15,4)(-17,10)(2,12)(6,8,14)
Multiloop annotated with half-edges
11^2_19 annotated with half-edges