$11^{1}_{2}$ - Minimal pinning sets
Pinning sets for 11^1_2 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_2 Pinning data
Pinning number of this loop: 7
Total number of pinning sets: 16
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: 2.74309
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, 4, 5, 6, 10}
7
[2, 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
7
1
0
0
2.0
8
0
0
4
2.44
9
0
0
6
2.78
10
0
0
4
3.05
11
0
0
1
3.27
Total
1
0
15
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 2, 3, 3, 8, 8]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,3],[0,3,2,0],[0,1,4,4],[0,5,5,1],[2,6,6,2],[3,7,7,3],[4,8,8,4],[5,8,8,5],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[17,8,18,9],[10,8,11,7],[1,16,2,17],[11,6,12,7],[15,2,16,3],[5,12,6,13],[3,14,4,15],[13,4,14,5]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,18,-14,-1)(11,2,-12,-3)(9,4,-10,-5)(5,8,-6,-9)(15,6,-16,-7)(3,10,-4,-11)(1,12,-2,-13)(17,14,-18,-15)(7,16,-8,-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,-13)(-2,11,-4,9,-6,15,-18,13)(-3,-11)(-5,-9)(-7,-17,-15)(-8,5,-10,3,-12,1,-14,17)(-16,7)(2,12)(4,10)(6,8,16)(14,18)
Loop annotated with half-edges
11^1_2 annotated with half-edges