$11^{1}_{64}$ - Minimal pinning sets
Pinning sets for 11^1_64 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_64 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, 6, 10}
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: [[1,2,2,3],[0,4,5,5],[0,6,7,0],[0,8,4,4],[1,3,3,8],[1,8,6,1],[2,5,7,7],[2,6,6,8],[3,7,5,4]]
PD code (use to draw this loop with SnapPy): [[13,18,14,1],[3,12,4,13],[17,14,18,15],[1,6,2,7],[7,2,8,3],[11,4,12,5],[15,11,16,10],[16,9,17,10],[5,8,6,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (5,18,-6,-1)(9,2,-10,-3)(17,4,-18,-5)(3,6,-4,-7)(14,7,-15,-8)(8,13,-9,-14)(1,10,-2,-11)(15,12,-16,-13)(11,16,-12,-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,-11,-17,-5)(-2,9,13,-16,11)(-3,-7,14,-9)(-4,17,-12,15,7)(-6,3,-10,1)(-8,-14)(-13,8,-15)(-18,5)(2,10)(4,6,18)(12,16)
Loop annotated with half-edges
11^1_64 annotated with half-edges