$10^{1}_{19}$ - Minimal pinning sets
Pinning sets for 10^1_19 Minimal pinning semi-lattice
(y-axis: cardinality)
Pinning semi lattice for 10^1_19 Pinning data
Pinning number of this loop: 4
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: 2.8189
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)
• {2, 3, 5, 9}
4
[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
4
1
0
0
2.0
5
0
0
6
2.4
6
0
0
15
2.67
7
0
0
20
2.86
8
0
0
15
3.0
9
0
0
6
3.11
10
0
0
1
3.2
Total
1
0
63
Other information about this loop Properties
Region degree sequence: [2, 2, 2, 2, 3, 3, 4, 4, 5, 5]
Minimal region degree: 2
Is multisimple: No
Combinatorial encoding data
Plantri embedding: [[1,2,2,3],[0,4,5,2],[0,1,6,0],[0,6,4,4],[1,3,3,5],[1,4,7,7],[2,7,7,3],[5,6,6,5]]
PD code (use to draw this loop with SnapPy): [[16,5,1,6],[6,3,7,4],[4,15,5,16],[1,10,2,11],[11,2,12,3],[7,12,8,13],[9,14,10,15],[8,14,9,13]]
Permutation representation (action on half-edges):
Vertex permutation $\sigma=$ (9,16,-10,-1)(4,1,-5,-2)(14,3,-15,-4)(15,8,-16,-9)(5,10,-6,-11)(11,6,-12,-7)(7,12,-8,-13)(2,13,-3,-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 $\varphi=(\sigma\epsilon)^{-1}=$ (-1,4,-15,-9)(-2,-14,-4)(-3,14)(-5,-11,-7,-13,2)(-6,11)(-8,15,3,13)(-10,5,1)(-12,7)(-16,9)(6,10,16,8,12)
Loop annotated with half-edges
10^1_19 annotated with half-edges