$11^{2}_{28}$ - Minimal pinning sets
Pinning sets for 11^2_28 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_28 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90403
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 5, 8, 9}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 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
2
0
0
2.2
6
0
0
11
2.55
7
0
0
25
2.79
8
0
0
30
2.97
9
0
0
20
3.1
10
0
0
7
3.2
11
0
0
1
3.27
Total
2
0
94
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,3,4,4],[0,5,6,6],[0,6,1,0],[1,7,8,1],[2,8,8,7],[2,7,3,2],[4,6,5,8],[4,7,5,5]]
PD code (use to draw this multiloop with SnapPy): [[4,18,1,5],[5,17,6,16],[9,3,10,4],[17,1,18,2],[6,15,7,16],[13,8,14,9],[2,10,3,11],[11,14,12,15],[7,12,8,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,1,-5,-2)(12,3,-13,-4)(8,17,-9,-18)(4,5,-1,-6)(16,7,-17,-8)(6,9,-7,-10)(15,10,-16,-11)(11,14,-12,-15)(2,13,-3,-14)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,18,-9,6)(-2,-14,11,-16,-8,-18)(-3,12,14)(-4,-6,-10,15,-12)(-5,4,-13,2)(-7,16,10)(-11,-15)(-17,8)(1,5)(3,13)(7,9,17)
Multiloop annotated with half-edges
11^2_28 annotated with half-edges