$11^{2}_{24}$ - Minimal pinning sets
Pinning sets for 11^2_24 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_24 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, 3, 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: [[1,2,3,4],[0,5,5,6],[0,7,3,3],[0,2,2,8],[0,6,5,5],[1,4,4,1],[1,4,8,7],[2,6,8,8],[3,7,7,6]]
PD code (use to draw this multiloop with SnapPy): [[11,14,12,1],[3,10,4,11],[13,18,14,15],[12,18,13,17],[1,8,2,9],[9,2,10,3],[4,8,5,7],[15,7,16,6],[16,5,17,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,14,-8,-1)(16,3,-17,-4)(4,15,-5,-16)(5,2,-6,-3)(13,6,-14,-7)(1,8,-2,-9)(9,12,-10,-13)(17,10,-18,-11)(11,18,-12,-15)
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,-7)(-2,5,15,-12,9)(-3,16,-5)(-4,-16)(-6,13,-10,17,3)(-8,1)(-11,-15,4,-17)(-14,7)(-18,11)(2,8,14,6)(10,12,18)
Multiloop annotated with half-edges
11^2_24 annotated with half-edges