$10^{1}_{10}$ - Minimal pinning sets
Pinning sets for 10^1_10 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_10 Pinning data
Pinning number of this loop: 5
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: 2.7622
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, 5, 6, 7}
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
5
2.4
7
0
0
10
2.69
8
0
0
10
2.9
9
0
0
5
3.07
10
0
0
1
3.2
Total
1
0
31
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 3, 3, 4, 5, 7]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,1,2,2],[0,3,4,0],[0,5,5,0],[1,6,6,4],[1,3,7,5],[2,4,7,2],[3,7,7,3],[4,6,6,5]]
PD code (use to draw this loop with SnapPy): [[16,9,1,10],[10,15,11,16],[8,1,9,2],[5,14,6,15],[11,6,12,7],[2,7,3,8],[13,4,14,5],[12,4,13,3]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (16,9,-1,-10)(10,1,-11,-2)(8,3,-9,-4)(15,4,-16,-5)(13,6,-14,-7)(2,11,-3,-12)(7,12,-8,-13)(5,14,-6,-15)
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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10)(-2,-12,7,-14,5,-16,-10)(-3,8,12)(-4,15,-6,13,-8)(-5,-15)(-7,-13)(-9,16,4)(-11,2)(1,9,3,11)(6,14)
Loop annotated with half-edges
10^1_10 annotated with half-edges