$11^{3}_{4}$ - Minimal pinning sets
Pinning sets for 11^3_4 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^3_4 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, 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],[2,8,6,6],[2,5,5,7],[4,6,8,8],[4,7,7,5]]
PD code (use to draw this multiloop with SnapPy): [[3,8,4,1],[2,14,3,9],[7,4,8,5],[1,10,2,9],[10,13,11,14],[5,15,6,18],[6,17,7,18],[12,16,13,17],[11,16,12,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,2,-6,-3)(1,6,-2,-7)(11,14,-12,-9)(8,9,-1,-10)(10,7,-11,-8)(17,12,-18,-13)(13,18,-14,-15)(4,15,-5,-16)(16,3,-17,-4)
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,-7,10)(-2,5,15,-14,11,7)(-3,16,-5)(-4,-16)(-6,1,9,-12,17,3)(-8,-10)(-9,8,-11)(-13,-15,4,-17)(-18,13)(2,6)(12,14,18)
Multiloop annotated with half-edges
11^3_4 annotated with half-edges