$11^{1}_{47}$ - Minimal pinning sets
Pinning sets for 11^1_47 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_47 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 96
of which optimal: 2
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90403
on average over minimal pinning sets: 2.2
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 6, 8, 10}
5
[2, 2, 2, 2, 3]
2.20
B (optimal)
• {1, 2, 6, 7, 10}
5
[2, 2, 2, 2, 3]
2.20
Data for pinning sets in each cardinal
Cardinality
Optimal pinning sets
Minimal suboptimal pinning sets
Nonminimal pinning sets
Averaged mean-degree
5
2
0
0
2.2
6
0
0
11
2.55
7
0
0
25
2.79
8
0
0
30
2.97
9
0
0
20
3.1
10
0
0
7
3.2
11
0
0
1
3.27
Total
2
0
94
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,6,6],[0,6,6,7],[0,7,8,8],[1,8,7,1],[2,3,3,2],[3,5,8,4],[4,7,5,4]]
PD code (use to draw this loop with SnapPy): [[5,18,6,1],[4,9,5,10],[17,8,18,9],[6,16,7,15],[1,12,2,13],[10,3,11,4],[7,16,8,17],[11,14,12,15],[2,14,3,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,4,-14,-5)(18,5,-1,-6)(15,8,-16,-9)(9,16,-10,-17)(7,10,-8,-11)(11,2,-12,-3)(3,12,-4,-13)(1,14,-2,-15)(6,17,-7,-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,-15,-9,-17,6)(-2,11,-8,15)(-3,-13,-5,18,-7,-11)(-4,13)(-6,-18)(-10,7,17)(-12,3)(-14,1,5)(-16,9)(2,14,4,12)(8,10,16)
Loop annotated with half-edges
11^1_47 annotated with half-edges