$10^{1}_{25}$ - Minimal pinning sets
Pinning sets for 10^1_25 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_25 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, 3, 4, 7, 9}
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, 5, 5, 6]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,3,3],[0,4,4,2],[0,1,5,5],[0,6,6,0],[1,6,7,1],[2,7,7,2],[3,7,4,3],[4,6,5,5]]
PD code (use to draw this loop with SnapPy): [[5,16,6,1],[4,11,5,12],[15,10,16,11],[6,2,7,1],[12,3,13,4],[9,14,10,15],[2,8,3,7],[13,8,14,9]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (10,1,-11,-2)(5,16,-6,-1)(11,6,-12,-7)(13,8,-14,-9)(2,9,-3,-10)(7,12,-8,-13)(3,14,-4,-15)(15,4,-16,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,10,-3,-15,-5)(-2,-10)(-4,15)(-6,11,1)(-7,-13,-9,2,-11)(-8,13)(-12,7)(-14,3,9)(-16,5)(4,14,8,12,6,16)
Loop annotated with half-edges
10^1_25 annotated with half-edges