$11^{1}_{90}$ - Minimal pinning sets
Pinning sets for 11^1_90 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_90 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, 2, 4, 5, 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, 4, 4, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,5],[0,6,6,7],[0,7,7,0],[1,8,8,1],[1,8,6,6],[2,5,5,2],[2,8,3,3],[4,7,5,4]]
PD code (use to draw this loop with SnapPy): [[18,11,1,12],[12,5,13,6],[8,17,9,18],[10,1,11,2],[4,13,5,14],[6,15,7,16],[16,7,17,8],[9,3,10,2],[14,3,15,4]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (7,18,-8,-1)(11,2,-12,-3)(13,6,-14,-7)(17,8,-18,-9)(1,10,-2,-11)(3,12,-4,-13)(5,14,-6,-15)(15,4,-16,-5)(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,-11,-3,-13,-7)(-2,11)(-4,15,-6,13)(-5,-15)(-8,17,-10,1)(-9,-17)(-12,3)(-14,5,-16,9,-18,7)(2,10,16,4,12)(6,14)(8,18)
Loop annotated with half-edges
11^1_90 annotated with half-edges