$11^{1}_{4}$ - Minimal pinning sets
Pinning sets for 11^1_4 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_4 Pinning data
Pinning number of this loop: 7
Total number of pinning sets: 16
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: 2.74309
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, 7, 8, 10}
7
[2, 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
7
1
0
0
2.0
8
0
0
4
2.44
9
0
0
6
2.78
10
0
0
4
3.05
11
0
0
1
3.27
Total
1
0
15
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 5, 5, 6, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,5,5],[0,6,6,4],[0,7,7,0],[1,7,7,2],[1,8,8,1],[2,8,8,2],[3,4,4,3],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[13,8,14,9],[17,4,18,5],[10,2,11,1],[3,12,4,13],[7,14,8,15],[5,16,6,17],[2,12,3,11],[15,6,16,7]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,1,-15,-2)(12,3,-13,-4)(10,5,-11,-6)(8,17,-9,-18)(18,9,-1,-10)(4,11,-5,-12)(2,13,-3,-14)(6,15,-7,-16)(16,7,-17,-8)
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,-3,12,-5,10)(-2,-14)(-4,-12)(-6,-16,-8,-18,-10)(-7,16)(-9,18)(-11,4,-13,2,-15,6)(-17,8)(1,9,17,7,15)(3,13)(5,11)
Loop annotated with half-edges
11^1_4 annotated with half-edges