$11^{1}_{37}$ - Minimal pinning sets
Pinning sets for 11^1_37 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_37 Pinning data
Pinning number of this loop: 4
Total number of pinning sets: 128
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: 2.89692
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, 3, 5, 6}
4
[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
4
1
0
0
2.0
5
0
0
7
2.4
6
0
0
21
2.67
7
0
0
35
2.86
8
0
0
35
3.0
9
0
0
21
3.11
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
0
127
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 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],[0,5,6,7],[0,7,8,4],[1,3,5,1],[2,4,6,6],[2,5,5,8],[2,8,8,3],[3,7,7,6]]
PD code (use to draw this loop with SnapPy): [[7,18,8,1],[17,6,18,7],[8,11,9,12],[1,4,2,5],[5,16,6,17],[10,15,11,16],[9,15,10,14],[12,3,13,4],[2,13,3,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (10,1,-11,-2)(17,2,-18,-3)(15,4,-16,-5)(6,9,-7,-10)(18,11,-1,-12)(12,7,-13,-8)(8,13,-9,-14)(3,14,-4,-15)(5,16,-6,-17)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10,-7,12)(-2,17,-6,-10)(-3,-15,-5,-17)(-4,15)(-8,-14,3,-18,-12)(-9,6,16,4,14)(-11,18,2)(-13,8)(-16,5)(1,11)(7,9,13)
Loop annotated with half-edges
11^1_37 annotated with half-edges