$11^{1}_{88}$ - Minimal pinning sets
Pinning sets for 11^1_88 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_88 Pinning data
Pinning number of this loop: 6
Total number of pinning sets: 32
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: 2.78769
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, 7, 8, 10}
6
[2, 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
6
1
0
0
2.0
7
0
0
5
2.4
8
0
0
10
2.7
9
0
0
10
2.93
10
0
0
5
3.12
11
0
0
1
3.27
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 4, 4, 6, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,3,0],[0,4,4,0],[1,5,6,1],[2,6,7,2],[3,7,7,8],[3,8,8,4],[4,8,5,5],[5,7,6,6]]
PD code (use to draw this loop with SnapPy): [[7,18,8,1],[17,6,18,7],[8,2,9,1],[5,16,6,17],[2,10,3,9],[13,4,14,5],[15,10,16,11],[3,12,4,13],[14,12,15,11]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,2,-12,-3)(15,4,-16,-5)(7,18,-8,-1)(13,8,-14,-9)(9,12,-10,-13)(1,10,-2,-11)(3,14,-4,-15)(5,16,-6,-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,-11,-3,-15,-5,-17,-7)(-2,11)(-4,15)(-6,17)(-8,13,-10,1)(-9,-13)(-12,9,-14,3)(-16,5)(-18,7)(2,10,12)(4,14,8,18,6,16)
Loop annotated with half-edges
11^1_88 annotated with half-edges