$11^{1}_{17}$ - Minimal pinning sets
Pinning sets for 11^1_17 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_17 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, 2, 3, 4, 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, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,5,5,6],[0,6,7,4],[1,3,5,1],[2,4,7,2],[2,8,8,3],[3,8,8,5],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[13,18,14,1],[17,12,18,13],[14,6,15,5],[1,10,2,11],[11,16,12,17],[6,16,7,15],[9,4,10,5],[2,8,3,7],[3,8,4,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (6,1,-7,-2)(2,11,-3,-12)(4,17,-5,-18)(18,5,-1,-6)(16,7,-17,-8)(14,9,-15,-10)(12,3,-13,-4)(8,13,-9,-14)(10,15,-11,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,6)(-2,-12,-4,-18,-6)(-3,12)(-5,18)(-7,16,-11,2)(-8,-14,-10,-16)(-9,14)(-13,8,-17,4)(-15,10)(1,5,17,7)(3,11,15,9,13)
Loop annotated with half-edges
11^1_17 annotated with half-edges