$11^{2}_{34}$ - Minimal pinning sets
Pinning sets for 11^2_34 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_34 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, 2, 5, 6}
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],[0,5,5,2],[0,1,6,7],[0,8,8,4],[0,3,7,6],[1,6,6,1],[2,5,5,4],[2,4,8,8],[3,7,7,3]]
PD code (use to draw this multiloop with SnapPy): [[10,5,1,6],[6,11,7,18],[9,17,10,18],[4,14,5,15],[1,14,2,13],[11,8,12,7],[12,8,13,9],[2,16,3,17],[15,3,16,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,10,-12,-1)(7,2,-8,-3)(4,15,-5,-16)(16,5,-17,-6)(17,8,-18,-9)(1,18,-2,-11)(9,12,-10,-13)(6,13,-7,-14)(14,3,-15,-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,-11)(-2,7,13,-10,11)(-3,14,-7)(-4,-16,-6,-14)(-5,16)(-8,17,5,15,3)(-9,-13,6,-17)(-12,9,-18,1)(-15,4)(2,18,8)(10,12)
Multiloop annotated with half-edges
11^2_34 annotated with half-edges