$11^{2}_{29}$ - Minimal pinning sets
Pinning sets for 11^2_29 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^2_29 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, 3, 5, 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, 5, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,3,4],[0,5,6,0],[0,7,1,1],[1,8,8,5],[2,4,6,6],[2,5,5,7],[3,6,8,8],[4,7,7,4]]
PD code (use to draw this multiloop with SnapPy): [[3,8,4,1],[2,18,3,9],[7,4,8,5],[1,10,2,9],[12,17,13,18],[5,13,6,14],[14,6,15,7],[10,15,11,16],[16,11,17,12]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,2,-6,-3)(15,4,-16,-5)(1,6,-2,-7)(17,12,-18,-13)(3,14,-4,-15)(11,16,-12,-17)(13,18,-14,-9)(8,9,-1,-10)(10,7,-11,-8)
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,-16,11,7)(-3,-15,-5)(-4,15)(-6,1,9,-14,3)(-8,-10)(-9,8,-11,-17,-13)(-12,17)(-18,13)(2,6)(4,14,18,12,16)
Multiloop annotated with half-edges
11^2_29 annotated with half-edges