$11^{1}_{36}$ - Minimal pinning sets
Pinning sets for 11^1_36 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_36 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 100
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: 2.9752
on average over minimal pinning sets: 2.49286
on average over optimal pinning sets: 2.4
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 4, 5, 7}
5
[2, 2, 2, 3, 3]
2.40
a (minimal)
• {1, 2, 4, 5, 6, 9}
6
[2, 2, 2, 3, 3, 3]
2.50
b (minimal)
• {1, 3, 4, 5, 7, 10}
6
[2, 2, 2, 3, 3, 3]
2.50
c (minimal)
• {1, 3, 4, 5, 6, 9, 10}
7
[2, 2, 2, 3, 3, 3, 3]
2.57
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
2.4
6
0
2
6
2.62
7
0
1
23
2.82
8
0
0
34
3.0
9
0
0
24
3.14
10
0
0
8
3.23
11
0
0
1
3.27
Total
1
3
96
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,3,4,4],[0,5,3,0],[0,2,5,1],[1,6,7,1],[2,8,6,3],[4,5,8,7],[4,6,8,8],[5,7,7,6]]
PD code (use to draw this loop with SnapPy): [[7,18,8,1],[6,15,7,16],[17,8,18,9],[1,17,2,16],[14,5,15,6],[9,3,10,2],[10,13,11,14],[11,4,12,5],[3,12,4,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(11,2,-12,-3)(14,5,-15,-6)(18,9,-1,-10)(7,10,-8,-11)(3,12,-4,-13)(13,16,-14,-17)(4,15,-5,-16)(17,6,-18,-7)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8,10)(-2,11,-8)(-3,-13,-17,-7,-11)(-4,-16,13)(-5,14,16)(-6,17,-14)(-9,18,6,-15,4,12,2)(-10,7,-18)(-12,3)(1,9)(5,15)
Loop annotated with half-edges
11^1_36 annotated with half-edges