$11^{4}_{1}$ - Minimal pinning sets
Pinning sets for 11^4_1 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^4_1 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, 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],[0,6,7,7],[0,7,4,0],[1,3,5,1],[1,4,8,6],[2,5,8,8],[2,8,3,2],[5,7,6,6]]
PD code (use to draw this multiloop with SnapPy): [[4,8,1,5],[5,9,6,14],[3,18,4,15],[7,1,8,2],[9,7,10,6],[10,13,11,14],[15,11,16,12],[17,2,18,3],[12,16,13,17]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,4,-6,-1)(18,3,-15,-4)(2,15,-3,-16)(17,12,-18,-13)(13,10,-14,-11)(11,16,-12,-17)(7,14,-8,-9)(9,8,-10,-5)(1,6,-2,-7)
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,-9,-5)(-2,-16,11,-14,7)(-3,18,12,16)(-4,5,-10,13,-18)(-6,1)(-8,9)(-11,-17,-13)(-12,17)(-15,2,6,4)(3,15)(8,14,10)
Multiloop annotated with half-edges
11^4_1 annotated with half-edges