$11^{3}_{11}$ - Minimal pinning sets
Pinning sets for 11^3_11 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^3_11 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)
• {2, 3, 6, 11}
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, 4, 4, 4, 4, 4, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,6],[0,6,7,7],[0,7,4,4],[0,3,3,5],[1,4,8,1],[1,8,8,2],[2,8,3,2],[5,7,6,6]]
PD code (use to draw this multiloop with SnapPy): [[10,3,1,4],[4,11,5,14],[9,18,10,15],[2,7,3,8],[1,7,2,6],[11,6,12,5],[13,15,14,16],[17,8,18,9],[12,17,13,16]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(3,12,-4,-13)(4,9,-5,-10)(10,5,-1,-6)(15,6,-16,-7)(11,2,-12,-3)(18,13,-15,-14)(7,16,-8,-17)(14,17,-11,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,16,6)(-2,11,17,-8)(-3,-13,18,-11)(-4,-10,-6,15,13)(-5,10)(-7,-17,14,-15)(-9,4,12,2)(-12,3)(-14,-18)(-16,7)(1,5,9)
Multiloop annotated with half-edges
11^3_11 annotated with half-edges