$11^{1}_{89}$ - Minimal pinning sets
Pinning sets for 11^1_89 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_89 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 32
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: 2.78769
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, 5, 8}
6
[2, 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
6
1
0
0
2.0
7
0
0
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 4, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,4,0],[0,4,5,5],[0,6,7,7],[1,7,2,1],[2,8,8,2],[3,8,8,7],[3,6,4,3],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[5,18,6,1],[17,4,18,5],[6,16,7,15],[1,10,2,11],[3,16,4,17],[7,14,8,15],[9,12,10,13],[2,12,3,11],[13,8,14,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,1,-15,-2)(10,5,-11,-6)(16,7,-17,-8)(8,17,-9,-18)(6,9,-7,-10)(4,11,-5,-12)(12,3,-13,-4)(18,13,-1,-14)(2,15,-3,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,14)(-2,-16,-8,-18,-14)(-3,12,-5,10,-7,16)(-4,-12)(-6,-10)(-9,6,-11,4,-13,18)(-15,2)(-17,8)(1,13,3,15)(5,11)(7,9,17)
Loop annotated with half-edges
11^1_89 annotated with half-edges