$11^{1}_{85}$ - Minimal pinning sets
Pinning sets for 11^1_85 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_85 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, 3, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,4,2,0],[0,1,5,5],[0,6,7,7],[1,7,8,8],[2,6,6,2],[3,5,5,8],[3,8,4,3],[4,7,6,4]]
PD code (use to draw this loop with SnapPy): [[11,18,12,1],[17,10,18,11],[12,10,13,9],[1,7,2,6],[3,16,4,17],[13,8,14,9],[7,14,8,15],[2,5,3,6],[15,4,16,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,2,-14,-3)(18,3,-1,-4)(4,17,-5,-18)(11,6,-12,-7)(7,10,-8,-11)(15,8,-16,-9)(5,12,-6,-13)(1,14,-2,-15)(9,16,-10,-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,-15,-9,-17,4)(-2,13,-6,11,-8,15)(-3,18,-5,-13)(-4,-18)(-7,-11)(-10,7,-12,5,17)(-14,1,3)(-16,9)(2,14)(6,12)(8,10,16)
Loop annotated with half-edges
11^1_85 annotated with half-edges