$11^{1}_{13}$ - Minimal pinning sets
Pinning sets for 11^1_13 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_13 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 64
of which optimal: 1
of which minimal: 1
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.83846
on average over minimal pinning sets: 2.0
on average over optimal pinning sets: 2.0
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 4, 5, 8, 10}
5
[2, 2, 2, 2, 2]
2.00
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
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,5,6,6],[0,7,7,0],[1,7,5,1],[1,4,8,2],[2,8,8,2],[3,8,4,3],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[5,18,6,1],[13,4,14,5],[17,10,18,11],[6,2,7,1],[3,12,4,13],[14,12,15,11],[9,16,10,17],[2,8,3,7],[15,8,16,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(5,18,-6,-1)(13,6,-14,-7)(15,8,-16,-9)(9,12,-10,-13)(1,10,-2,-11)(7,14,-8,-15)(3,16,-4,-17)(17,4,-18,-5)
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,-3,-17,-5)(-2,11)(-4,17)(-6,13,-10,1)(-7,-15,-9,-13)(-8,15)(-12,9,-16,3)(-14,7)(-18,5)(2,10,12)(4,16,8,14,6,18)
Loop annotated with half-edges
11^1_13 annotated with half-edges