$11^{1}_{79}$ - Minimal pinning sets
Pinning sets for 11^1_79 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_79 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 112
of which optimal: 3
of which minimal: 3
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.91313
on average over minimal pinning sets: 2.26667
on average over optimal pinning sets: 2.26667
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 6, 9}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 3, 5, 6}
5
[2, 2, 2, 2, 3]
2.20
C (optimal)
• {1, 2, 3, 6, 8}
5
[2, 2, 2, 2, 4]
2.40
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
3
0
0
2.27
6
0
0
15
2.6
7
0
0
31
2.83
8
0
0
34
2.99
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
3
0
109
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,6,7],[0,7,4,4],[0,3,3,8],[1,8,8,1],[2,8,7,7],[2,6,6,3],[4,6,5,5]]
PD code (use to draw this loop with SnapPy): [[18,3,1,4],[4,13,5,14],[14,17,15,18],[9,2,10,3],[1,10,2,11],[12,5,13,6],[7,16,8,17],[15,8,16,9],[11,7,12,6]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (8,1,-9,-2)(2,7,-3,-8)(11,4,-12,-5)(15,6,-16,-7)(18,9,-1,-10)(3,12,-4,-13)(10,13,-11,-14)(5,16,-6,-17)(14,17,-15,-18)
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,-3,-13,10)(-2,-8)(-4,11,13)(-5,-17,14,-11)(-6,15,17)(-7,2,-9,18,-15)(-10,-14,-18)(-12,3,7,-16,5)(1,9)(4,12)(6,16)
Loop annotated with half-edges
11^1_79 annotated with half-edges