$11^{1}_{25}$ - Minimal pinning sets
Pinning sets for 11^1_25 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_25 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 200
of which optimal: 1
of which minimal: 4
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 3.04458
on average over minimal pinning sets: 2.59167
on average over optimal pinning sets: 2.5
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 10}
4
[2, 2, 3, 3]
2.50
a (minimal)
• {1, 2, 4, 8, 11}
5
[2, 2, 3, 3, 3]
2.60
b (minimal)
• {1, 2, 3, 6, 10}
5
[2, 2, 3, 3, 3]
2.60
c (minimal)
• {1, 2, 3, 6, 8, 11}
6
[2, 2, 3, 3, 3, 3]
2.67
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
2.5
5
0
2
7
2.71
6
0
1
31
2.88
7
0
0
58
3.01
8
0
0
58
3.12
9
0
0
32
3.19
10
0
0
9
3.24
11
0
0
1
3.27
Total
1
3
196
Other information about this loop Properties
Region degree sequence: [2, 2, 3, 3, 3, 3, 3, 3, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,5,5],[0,6,7,3],[0,2,7,8],[0,6,5,1],[1,4,6,1],[2,5,4,8],[2,8,8,3],[3,7,7,6]]
PD code (use to draw this loop with SnapPy): [[18,11,1,12],[12,4,13,3],[6,17,7,18],[7,10,8,11],[1,5,2,4],[13,2,14,3],[14,5,15,6],[9,16,10,17],[8,16,9,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,18,-12,-1)(1,10,-2,-11)(2,17,-3,-18)(12,3,-13,-4)(5,8,-6,-9)(16,9,-17,-10)(13,6,-14,-7)(7,14,-8,-15)(4,15,-5,-16)
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,-18,11)(-3,12,18)(-4,-16,-10,1,-12)(-5,-9,16)(-6,13,3,17,9)(-7,-15,4,-13)(-8,5,15)(-14,7)(-17,2,10)(6,8,14)
Loop annotated with half-edges
11^1_25 annotated with half-edges