$11^{1}_{16}$ - Minimal pinning sets
Pinning sets for 11^1_16 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_16 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 64
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: 2.83846
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, 5, 6, 10}
5
[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
5
1
0
0
2.0
6
0
0
6
2.39
7
0
0
15
2.67
8
0
0
20
2.88
9
0
0
15
3.04
10
0
0
6
3.17
11
0
0
1
3.27
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 4, 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],[0,4,5,6],[0,7,7,4],[1,3,2,1],[2,7,8,8],[2,8,8,7],[3,6,5,3],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[18,7,1,8],[8,17,9,18],[6,15,7,16],[1,11,2,10],[16,9,17,10],[12,5,13,6],[14,3,15,4],[11,3,12,2],[4,13,5,14]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (18,9,-1,-10)(12,1,-13,-2)(10,3,-11,-4)(16,5,-17,-6)(14,7,-15,-8)(8,17,-9,-18)(2,11,-3,-12)(4,13,-5,-14)(6,15,-7,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,12,-3,10)(-2,-12)(-4,-14,-8,-18,-10)(-5,16,-7,14)(-6,-16)(-9,18)(-11,2,-13,4)(-15,6,-17,8)(1,9,17,5,13)(3,11)(7,15)
Loop annotated with half-edges
11^1_16 annotated with half-edges