$11^{1}_{14}$ - Minimal pinning sets
Pinning sets for 11^1_14 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 11^1_14 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, 7, 8, 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, 4, 4, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,4,0],[0,5,5,0],[1,5,6,7],[1,7,6,5],[2,4,3,2],[3,4,8,8],[3,8,8,4],[6,7,7,6]]
PD code (use to draw this loop with SnapPy): [[9,18,10,1],[17,8,18,9],[10,2,11,1],[3,16,4,17],[7,12,8,13],[2,12,3,11],[15,6,16,7],[4,14,5,13],[5,14,6,15]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (13,4,-14,-5)(15,6,-16,-7)(9,18,-10,-1)(5,10,-6,-11)(11,2,-12,-3)(3,12,-4,-13)(1,14,-2,-15)(7,16,-8,-17)(17,8,-18,-9)
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,-7,-17,-9)(-2,11,-6,15)(-3,-13,-5,-11)(-4,13)(-8,17)(-10,5,-14,1)(-12,3)(-16,7)(-18,9)(2,14,4,12)(6,10,18,8,16)
Loop annotated with half-edges
11^1_14 annotated with half-edges