$11^{2}_{61}$ - Minimal pinning sets
Pinning sets for 11^2_61 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_61 Pinning data
Pinning number of this multiloop: 5
Total number of pinning sets: 64
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: 2.83846
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, 3, 8, 10}
5
[2, 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
5
1
0
0
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this multiloop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,5,6,7],[0,7,7,0],[1,8,8,5],[1,4,2,1],[2,8,8,7],[2,6,3,3],[4,6,6,4]]
PD code (use to draw this multiloop with SnapPy): [[12,18,1,13],[13,8,14,7],[15,11,16,12],[17,1,18,2],[8,5,9,6],[14,6,15,7],[10,3,11,4],[16,3,17,2],[4,9,5,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (3,12,-4,-1)(14,1,-15,-2)(2,13,-3,-14)(11,4,-12,-5)(15,6,-16,-7)(17,8,-18,-9)(9,16,-10,-17)(5,10,-6,-11)(7,18,-8,-13)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14,-3)(-2,-14)(-4,11,-6,15,1)(-5,-11)(-7,-13,2,-15)(-8,17,-10,5,-12,3,13)(-9,-17)(-16,9,-18,7)(4,12)(6,10,16)(8,18)
Multiloop annotated with half-edges
11^2_61 annotated with half-edges