$11^{1}_{32}$ - Minimal pinning sets
Pinning sets for 11^1_32 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_32 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 80
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.90697
on average over minimal pinning sets: 2.26667
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 5, 10}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 2, 3, 4, 7, 10}
6
[2, 2, 2, 2, 3, 3]
2.33
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
2.2
6
0
1
6
2.5
7
0
0
19
2.74
8
0
0
26
2.94
9
0
0
19
3.09
10
0
0
7
3.2
11
0
0
1
3.27
Total
1
1
78
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 3, 3, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,4,4,5],[0,6,7,3],[0,2,7,7],[0,5,1,1],[1,4,8,8],[2,8,8,7],[2,6,3,3],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[3,18,4,1],[2,9,3,10],[14,17,15,18],[4,15,5,16],[1,11,2,10],[11,8,12,9],[13,6,14,7],[16,5,17,6],[7,12,8,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (14,3,-15,-4)(11,4,-12,-5)(9,6,-10,-7)(18,7,-1,-8)(8,17,-9,-18)(5,10,-6,-11)(2,13,-3,-14)(12,15,-13,-16)(1,16,-2,-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,-17,8)(-2,-14,-4,11,-6,9,17)(-3,14)(-5,-11)(-7,18,-9)(-8,-18)(-10,5,-12,-16,1,7)(-13,2,16)(-15,12,4)(3,13,15)(6,10)
Loop annotated with half-edges
11^1_32 annotated with half-edges