$10^{1}_{1}$ - Minimal pinning sets
Pinning sets for 10^1_1 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_1 Pinning data
Pinning number of this loop: 6
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: 2.71339
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, 9}
6
[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
6
1
0
0
2.0
7
0
0
4
2.43
8
0
0
6
2.75
9
0
0
4
3.0
10
0
0
1
3.2
Total
1
0
15
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 2, 2, 3, 3, 7, 7]
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],[4,7,7,4],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[16,7,1,8],[8,15,9,16],[9,6,10,7],[1,14,2,15],[5,10,6,11],[13,2,14,3],[11,4,12,5],[3,12,4,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (11,16,-12,-1)(9,2,-10,-3)(7,4,-8,-5)(14,5,-15,-6)(3,8,-4,-9)(1,10,-2,-11)(15,12,-16,-13)(6,13,-7,-14)
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,-11)(-2,9,-4,7,13,-16,11)(-3,-9)(-5,14,-7)(-6,-14)(-8,3,-10,1,-12,15,5)(-13,6,-15)(2,10)(4,8)(12,16)
Loop annotated with half-edges
10^1_1 annotated with half-edges