$10^{1}_{11}$ - Minimal pinning sets
Pinning sets for 10^1_11 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_11 Pinning data
Pinning number of this loop: 5
Total number of pinning sets: 40
of which optimal: 1
of which minimal: 2
The mean region-degree (mean-degree) of a pinning set is
on average over all pinning sets: 2.8356
on average over minimal pinning sets: 2.26667
on average over optimal pinning sets: 2.2
Refined data for the minimal pinning sets
Pin label
Pin color
Regions
Cardinality
Degree sequence
Mean-degree
A (optimal)
• {1, 2, 3, 6, 9}
5
[2, 2, 2, 2, 3]
2.20
a (minimal)
• {1, 2, 3, 4, 5, 9}
6
[2, 2, 2, 2, 3, 3]
2.33
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
2.2
6
0
1
5
2.5
7
0
0
13
2.76
8
0
0
13
2.96
9
0
0
6
3.11
10
0
0
1
3.2
Total
1
1
38
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 3, 4, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,4],[0,5,5,2],[0,1,5,3],[0,2,6,6],[0,7,7,5],[1,4,2,1],[3,7,7,3],[4,6,6,4]]
PD code (use to draw this loop with SnapPy): [[16,5,1,6],[6,14,7,13],[15,12,16,13],[4,11,5,12],[1,9,2,8],[14,8,15,7],[10,3,11,4],[9,3,10,2]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,7,-1,-8)(8,1,-9,-2)(14,3,-15,-4)(5,12,-6,-13)(6,15,-7,-16)(2,9,-3,-10)(13,10,-14,-11)(11,4,-12,-5)
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)
Face permutation $\varphi=(\sigma\epsilon)^{-1}=$ (-1,8)(-2,-10,13,-6,-16,-8)(-3,14,10)(-4,11,-14)(-5,-13,-11)(-7,16)(-9,2)(-12,5)(-15,6,12,4)(1,7,15,3,9)
Loop annotated with half-edges
10^1_11 annotated with half-edges