$11^{1}_{29}$ - Minimal pinning sets
Pinning sets for 11^1_29 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_29 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 200
of which optimal: 1
of which minimal: 5
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.98939
on average over minimal pinning sets: 2.53
on average over optimal pinning sets: 2.25
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 6, 10}
4
[2, 2, 2, 3]
2.25
a (minimal)
• {1, 2, 4, 10, 11}
5
[2, 2, 2, 3, 4]
2.60
b (minimal)
• {1, 2, 3, 10, 11}
5
[2, 2, 2, 3, 3]
2.40
c (minimal)
• {1, 2, 4, 7, 10}
5
[2, 2, 2, 4, 4]
2.80
d (minimal)
• {1, 2, 3, 7, 10}
5
[2, 2, 2, 3, 4]
2.60
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
2.25
5
0
4
7
2.58
6
0
0
37
2.82
7
0
0
60
2.98
8
0
0
54
3.09
9
0
0
28
3.17
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
4
195
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,5,6,3],[0,2,7,7],[0,5,1,1],[1,4,8,2],[2,8,8,7],[3,6,8,3],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[3,18,4,1],[13,2,14,3],[17,10,18,11],[4,10,5,9],[1,12,2,13],[14,12,15,11],[7,16,8,17],[5,8,6,9],[15,6,16,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,18,-12,-1)(13,4,-14,-5)(3,6,-4,-7)(7,2,-8,-3)(15,8,-16,-9)(9,12,-10,-13)(17,10,-18,-11)(5,14,-6,-15)(1,16,-2,-17)
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,-17,-11)(-2,7,-4,13,-10,17)(-3,-7)(-5,-15,-9,-13)(-6,3,-8,15)(-12,9,-16,1)(-14,5)(-18,11)(2,16,8)(4,6,14)(10,12,18)
Loop annotated with half-edges
11^1_29 annotated with half-edges