$11^{1}_{83}$ - Minimal pinning sets
Pinning sets for 11^1_83
Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_83
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, 3, 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, 3, 4, 4, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,5,6],[0,6,7,0],[1,5,5,1],[2,4,4,7],[2,8,8,3],[3,8,8,5],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[18,13,1,14],[14,7,15,8],[8,17,9,18],[12,1,13,2],[6,15,7,16],[16,5,17,6],[9,3,10,2],[4,11,5,12],[3,11,4,10]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(11,4,-12,-5)(7,18,-8,-1)(1,8,-2,-9)(15,10,-16,-11)(3,12,-4,-13)(5,14,-6,-15)(9,16,-10,-17)(17,6,-18,-7)
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,-9,-17,-7)(-2,13,-4,11,-16,9)(-3,-13)(-5,-15,-11)(-6,17,-10,15)(-8,1)(-12,3,-14,5)(-18,7)(2,8,18,6,14)(4,12)(10,16)
Loop annotated with half-edges
11^1_83 annotated with half-edges